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CATALOGUE 

OF 

SCIENTIFIC PAPERS 

1800-1900 



SUBJECT INDEX 



VOLUME I 



PURE MATHEMATICS 



CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, 

C. F. CLAY, MANAGER. 

aotlbon : FETTEE LANE, E.G. 

Iagflota: 30, WELLINGTON STREET. 




F. A. BEOCKHAUS. 
eta 2ork: G. P. PUTNAM'S SONS. 
Bombag anto Calcutta: MACMILLAN AND CO., LTD. 



[All Rights reserved.] 



ROYAL SOCIETY OF LONDON 
CATALOGUE 

OF 

SCIENTIFIC PAPERS 
1800-1900 



SUBJECT INDEX 

VOLUME I 

PURE MATHEMATICS 



CAMBRIDGE : 

AT THE UNIVERSITY PRESS 
1908 






ARRANGED FOR A COMMITTEE OF THE ROYAL SOCIETY 
UNDER THE SUPERINTENDENCE OF 

HERBERT M C LEOD, LL.D., F.R.S. 

DIRECTOR OF THE CATALOGUE 
with the assistance of 

R. J. DALLAS, M.A. 

KING'S COLLEGE, CAMBRIDGE 






PREFACE 

~VT7"HEN the plan for a Catalogue of Scientific Papers was drawn up in 
* 1857 by the Royal Society, it was also contemplated that a Subject 
Index to the papers should be made. During the compilation of the well 
known twelve volumes of the Catalogue of Authors (1800 1883) much 
material was collected for the Subject Index by the Committee of the 
Society which had charge of the work, but nothing was printed. 

In 1898 it was determined to undertake the continuation for the period 
1884 1900, and at the same time to prepare material for a Subject Index 
for these last seventeen years of the century. It was afterwards decided 
that one Index should be made to the papers of the whole of the Nineteenth 
Century ; and to bring this Index into relation with the International 
Catalogue of Scientific Literature, which deals with publications subsequent 
to 1900, the Index was to be arranged in accordance with the schedules of 
the different sciences which form the basis of the International Catalogue. 

The extent of the work for the period 18841900 proved to be so 
great that the resources of the Royal Society would have been quite 
inadequate for its completion. Its continuation has been made possible by 
liberal donations received from various sources. The Catalogue is especially 
indebted to Dr Ludwig Mond, F.R.S., a member of the Committee entrusted 
with its preparation, who has encouraged and forwarded its progress in every 
way for many years past; in particular, in addition to similar generous 
donations at earlier stages, Dr Mond recently undertook to provide an 
extremely liberal subsidy during the three years 1907 9, which has enabled 
the work to be pressed forward rapidly. 

The Subject Index will be published as separate Index-volumes for each 
of the seventeen Sciences of the Schedules of the International Catalogue, 
viz. Mathematics, Mechanics, Physics, Chemistry, Astronomy, Meteorology, 
Mineralogy, Geology, Geography, Palaeontology, Biology, Botany, Zoology, 
Anatomy, Anthropology, Physiology, and Bacteriology. 

The practical advantage which will accrue from thus classifying the 
literature of each Science seems to be amply sufficient, in spite of un- 
avoidable imperfections, to justify the great expense that has been involved. 
In the past a student interested in a single branch of the subject would 
probably consult special Treatises and Reports from which he could obtain 
references to the more important memoirs. But it often happens that 
such references are transferred simply from one treatise to another, and 



Preface 

experience shows that important contributions that have once dropped out 
of sight may for a long time, or indeed ever afterwards, be overlooked. 
When the whole literature is set out systematically and exhaustively under 
appropriate headings as in the present volume, such accidents are guarded 
against so far as seems to be possible. 

The present volume dealing with Pure Mathematics is the first instal- 
ment of the Subject Index : it contains 38748 entries referring to 700 serials. 
It is believed that these entries cover all the contents of the serials indexed 
with the exception of about 750 short notes (mostly falling under 6810 and 
7210) which were not thought of sufficient permanent interest to be entered. 

The Index titles for papers published from 1884 to 1900 inclusive have 
been made by Referees familiar with the subjects, who have consulted the 
original papers and have made the titles from the contents of the papers 
and not merely from their headings. It was intended that the Index entries 
for the papers from 1800 to 1883 should be made from the titles as printed 
in the Catalogue of Authors, but it was soon found that many of the titles 
were too indefinite for such minute classification, and reference has had to 
be made to the original papers in a large number of cases. The latter part 
of this work was commenced by the late Mr George Griffith of Harrow, whose 
untimely death was a great loss to the Committee. 

The entries in the Index are arranged so that reference can be made 
to the complete titles in the Catalogue of Scientific Papers. Generally the 
author's name together with the date will indicate the volume in which the 
title of the paper may be found. These clues are insufficient when the 
paper is anonymous or occurs in Volume XII or in the additions to 
Volume VI. They are also at fault for titles marked with an asterisk 
showing that they belong to previous volumes ; in these cases the number 
of the volume is given in the Index entry in small Roman numerals within 
brackets. 

When an error has been found in an author's name in the Catalogue, it 
is corrected in the Index by a reference made to the error. 

The Index contains references to some papers of dates earlier than 1884 
which were omitted in previous volumes of the Catalogue : these are 
indicated by an asterisk placed before the date ; the full titles of these 
papers will be given in the continuation of the Catalogue of Authors. 

When an author's personal name does not appear in the heading of an 
original paper, no attempt has been made to find the name for the Index, 
but this will be done for the Catalogue of Authors. 

The Catalogue of Authors for the period 1884 to 1900 is in preparation; 
the material will not however be quite complete until the Subject Indexes 
for the various Sciences have been reduced into order. 

Entries on the same subject are arranged, so far as possible, in order of 



Preface 

date irrespective of the authors' names, with the endeavour to present the 
subject in the historical form. This grouping of the entries, involving 
modifications of titles prepared by different Referees, or by the same Referee 
at different times, has been one of the most difficult problems in the 
preparation of the Index. 

The abbreviations of the names of the serials used in the Royal Society 
Catalogue have been further shortened for the Index. As the abbreviations 
are not uniform in all the volumes, it will be found that the same journal 
may be indicated by several different abbreviations, but in each case the 
one selected is that which was used in the volume in which the title of 
the paper occurs. 

In the case of serials commencing since 1883, the abbreviations adopted 
in the International Catalogue have been used as a guide. 

The list of serials will, it is hoped, be a valuable feature of the Index. 
It has been drawn up by the Director and contains the names of 701 serials 
from which the entries in the Index have been taken. Each title is pre- 
ceded by the abbreviation which represents the serial in the Index ; the 
date of commencement of the serial is given, and if it is extinct the date of 
the last volume is added. There are appended symbols representing the 
names of twenty-three British Libraries in some of which the serials may be 
found ; where the set is incomplete the symbol is followed by i. The in- 
formation from which this list has been compiled was obtained, in the first 
instance, from published catalogues ; subsequently the list was submitted 
to the custodians of many of the libraries, who kindly marked many serials 
which had not been found in the catalogues used. The thanks of the 
Committee for this valuable assistance are due to Mr F. Jenkinson of the 
Cambridge University Library, Mr E. W. B. Nicholson of the Bodleian 
Library, the Librarian of the Radcliffe Library, the Librarian of the 
Patent Office, Dr B. Daydon Jackson and Mr A. W. Kappel of the 
Linnean Society, Mr W. H. Wesley of the Royal Astronomical Society, 
Mr C. V. Crook of the Geological Museum, Mr F. W. Clifford of the 
Chemical Society, and Mr R. W. Chambers of University College, London ; 
Mr R. Lloyd Praeger obtained the information from the five libraries in 
Dublin, and Dr Hugh Marshall, F.R.S., from two libraries in Edinburgh 
and two in Glasgow. 

Although much care has been expended in making this list as accurate 
as possible, it is probable that some errors will still be found and the Director 
will be thankful to any one who will send corrections : portions of the list 
will be required for the subsequent volumes of the Index. 

The subjects are arranged under the registration numbers adopted in 
the International Catalogue; a copy of Schedule A, Mathematics, is pre- 
fixed to the Index, with indication of the pages on which the titles for the 

viz 



Preface 

different sections occur. It has occasionally been found convenient, in order 
to save repetition in printing, to group entries under a sub-heading which 
is not contained in the International Catalogue Schedule. Where this has 
been done the sub-heading is printed in italics. In some of these cases 
the words of the sub-heading are understood to exist before the entries 
following them, and consequently these entries commence with small letters. 
These minor classifications, being often made mechanically on the basis of 
the explicit mention of the sub-heading, are not to be taken as exhaustive ; 
cognate entries may be found elsewhere under the same main heading. The 
unit of classification is thus the complete numbered heading. 

The first portion of the present volume of the Index having been sent to 
press before the whole of the material had been sorted, some slips belonging 
to earlier sections were discovered during the arrangement of the later ones. 
These titles have been placed in an Appendix under their appropriate 
registration numbers. 

The following referees have assisted at various times in the preparation 
of the Subject Index in Pure Mathematics : the late Professor J. D. Everett, 
F.R.S., Mr R. J. Dallas, Miss Alice Everett, Mr R. Hargreaves, Miss W. M. 
Hudson, Mr H. Knapman, Miss E. Perrin and Mr G. Harold Wilson. The 
Committee is indebted to them for much valuable help. 

The arrangement of the contents of this volume for the press has been 
made by Mr R. J. Dallas, M.A., of King's College, Cambridge. To him and 
to Miss Brernner and the members of the Catalogue Staff thanks are due 
for careful and conscientious work. 

At the request of the other members of the Committee, Mr G. B. 
Mathews, F.R.S., examined the whole of the proof-sheets, and made sugges- 
tions for their improvement : he was also consulted from time to time about 
questions of arrangement, head lines and sub-headings. 

When the time for going to press approached, the Committee learned 
with much satisfaction that the Syndics of the Cambridge University Press 
were willing to undertake the complete risk of printing and publishing, as 
regards both the Catalogue of Scientific Papers and the Subject Index. It 
will be the care of the Committee, and it is hoped of the Scientific world 
generally, to use their best endeavours that this public-spirited action shall 
not result in financial loss. 

Finally the thanks of the Committee are due to the officials of the 
Cambridge Press for their unfailing courtesy in the discharge of a complex 
task. 

March 1908. 



viii 



SUBJECT INDEX OF PURE MATHEMATICS 



LIST OF SERIAL PUBLICATIONS 

WITH THE ABBEEVIATIONS OF THEIR TITLES USED IN THE INDEX, AND 
LIBRARIES WHERE THE SERIALS CAN BE CONSULTED. 

The date following the title of a serial indicates the year of its commencement ; if a second 
date is given it marks the termination of the serial. 

The letters following the dates indicate libraries where the serials are to be found: if the 
serial is incomplete, the symbol of the library is followed by i. 



B.M. British Museum. Glasg.P.S. 

Camb.P.S. Cambridge Philosophical Library. 

Camb.U. Cambridge University Library. Glasg.U. 

Chem.S. Chemical Society. Linn.S. 

Dub.N.L.I. National Library of Ireland,Dublin. Math.S. 

Dub.R.C.S. Royal College of Science, Dublin. N.H.M. 

Dub.R.D.S. Royal Dublin Society. Oxon.B. 

Dub.R.I.A. Royal Irish Academy, Dublin. Oxon.B. (R.) 

Dub.T.C. Trinity College, Dublin. Oxon.R. 

Edinb.R.S. Royal Society of Edinburgh. P.O. 

Edinb.U. Edinburgh University. R.A.S. 

Geol.M. Geological Survey Museum, Jer- R.S. 

myn St. U.C.L. 



Royal Philosophical Society of 

Glasgow. 

Glasgow University. 
Linnean Society. 
Mathematical Society. 
Natural History Museum. 
Bodleian, Oxford. 
Deposited in Radcliffe. 
Radcliffe, Oxford. 
Patent Office, London. 
Royal Astronomical Society. 
Royal Society. 
University College, London. 



Abv. Mm. a. Em 

Abv. 8. Mm. . 



A. C 

Ac. Caes. Leop. N. Acta . . 

Acireale Ac. At 

A. Cond. Pon. Chauss. .. 

A. Cons. Arts et IWet . 



Ac. Nt. C. NT. Acta 

Acta Mth 



. (Me"mou-es de la Societe d'Emulation d' Abbeville. Abbeville. 
Jl833 B.M. ; Camb.U.i. ; Dub.T.C.; Edinb.R.S.i.; Linn.S.i.; 

( N.H.M.i.; Oxon.B.i.; R.S.i. 
. Annales de Chimie, ou Recueil de Memoires concemant la Chimie 

et les Arts qui en dependent. Paris. 

1789 B.M.; Camb.U.; Chem.S.; Dub.R.D.S.i. ; Dub.T.C.i. ; 
Edinb.R.S.; Edinb.U.; N.H.M.; Oxon.B.i.(R.) ; P.O.; R.S. ; 
U.C.L. 
. Nova Acta physico-medica Academies Caes. Leopoldino-Carolinse 

Naturae Curiosorum. Erlangen, Bonn, Breslau. 
1758 Camb.P.S.; Camb.U.; Chem.S.i.; Dub.T.C.; Edinb.R.S.i.; 
Edinb.U.; Linn.S.i.; Math.S.i.; N.H.M.; Oxon.R.; R.A.S.*.; 
R.S.; U.C.L.i. 

See Ac. Nt. C. 1*. Acta n,,,l Caes. Z.eop. Ac. N. Acta. 
. Atti e Rendiconti dell' Accademia di Scienze, Lettere e Arti dei 

Zelanti e PP. dello Studio di Acireale. 
1890 Camb.P.S.i.; N.H.M.i.; R.S.i. 

. Annales des Conducteurs des Fonts et Chaussees ; recueil de 
memoires, etc., concemant le Service de Conducteurs des Fonts 
et Chaussees. Paris. 
1857 P.O. 
. Annales du Conservatoire des Arts et Metiers. Paris. 

1861 B.M.; Camb.U.; Glasg.P.S.i. ; Oxon.B.; P.O.; R.S. 
See Far. A. Cons. 

. See Ac. Caes. Loop. N. Acta and Caes. Leop. Ac. N. Acta. 
. Acta Mathematica. Stockholm. 

1882 B.M. ; Camb.P.S. ; Camb.U. ; Dub.T.C. ; Edinb.R.S. ; 
Edinb.U.; Glasg.U.; Math.S.; Oxon.R.; R.A.S.; R.S.; U.C.L. 

ix 



List of Serial Publications 



A. der Hydros 

A. diO 

Aer. J. 

A. Qen. Civ 



Aix Mm. 

Aix Mm. Ac. 
Alb. X. T 

Allelod. 8. T. 



Am. As. P. 



Am. Eng. & Railroad J, 

Amiens Ac. Mm 

Amiens Mm 

Amiens Mm. Ac 

Amiens Mm. Ac. Be. . 
A. Mines ... 



Am. X. T. 



Am. J. Be 



Am. Ph. 8. P. 



Am. Ph. a. T 



Annalen der Hydrographie und Maritimen Meteorologie. Heraus- 

gegeben von der Deutschen Seewarte in Hamburg. Berlin. 
1873 B.M.; P.O.i. 
Annali di Chimica. Milano. 
18451900. B.M.; Chem.S.i.; P.O.i. 
The Aeronautical Journal. London. 
1897 B.M.; Camb.U.i.; P.O.; B.S. 
Annales du G6nie Civil ; Becueil de MSmoires sur les Mathematiques 

pures et appliqu6es; 1'Astronomie, la Chimie, la Physique, etc. 

Paris. 

186280. B.M.; Camb.U.; Dub.B.C.S.i.; P.O. 
Annales Hydrographiques. Becueil d'avis, instructions, documents, 

et memoires relatifs a 1' Hydrographie et a la Navigation. Paris. 
1849 B.M.; Ebinb.B.S.i. ; Oxon.B. ; B.A.S.i.; E.S.i. 

i Memoires de PAcademie des Sciences, Agriculture, Arts et Belles- 
lettres. Aix. 
1819 B.M.; Dub.B.I.A.; N.H.M.i.; Oxon.B.i.; B.S.i. 
. Transactions of the Albany Institute. Albany. 

1830 B.M.; N.H.M.; B.S. 
.. The Transactions of the Allelodidactic Society. London. 

1848. B.S. 
. . Memoirs of the American Academy of Arts and Sciences. Cambridge 

and Boston. 

1785 B.M.i.; Camb.P.S.; Camb.U.; Dub.B.D.S.i.; Dub.E.I.A.i.; 
Dub.T.C.i.; Edinb.B.S.; Linn.S. ; N.H.M.; Oxon.B.; P.O.i.; 
R.A.S.; B.S.; U.C.L.i. 

See Boat. Am. Ac. Mm. <ui<l Boat. Mm. Am. Ac. 
.. Proceedings of the American Academy of Arts and Sciences. Boston. 
1846 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.B.D.S.; 
Edinb.E.S.; Glasg.P.S.; Glasg.U.i.; Linn.S.; N.H.M.; Oxon.B.; 
P.O.; B.A.S.; B.S.; U.C.L.i. 
,. Proceedings of the American Association for the Advancement of 

Science. Washington, Salem. 

1848 B.M.i.; Camb.P.S.; Camb.U.; Dub.B.I.A.; Edinb.B.S.i. ; 
Glasg.P.S.i.; Glasg.U.i.; Linn.S.; N.H.M.; Oxon.B.; Oxon.B.; 
P.O.; B.A.S.i.; B.S. 
. The American Chemist, a monthly Journal of theoretical Chemistry. 

New York. 

187177. Chem.S.i. ; N.H.M. ; P.O. 
American Engineer and Railroad Journal. New York. 
189395. B.M.; P.O. 

. /Memoires de 1'Academie des Sciences, Agriculture, Commerce, 
. J Belles-lettres, et Arts du departement de la Somme. Amiens. 
. 1 1835 B.M. ; Camb.U. ; Dub.T.C.i. ; N.H.M.i. ; Oxon.B.i. ; 
. ( B.S.i. 

. Annales des Mines, ou Becueil des Memoires sur 1'exploitation des 
Mines, et sur les Sciences et les Arts qui s'y rapportent. Paris. 

1817 B.M.; Camb.U.; Chem.S.i.; Dub.B.I.A.; Edinb.B.S.; 
Edinb.U.i.; Glasg.P.S.i.; N.H.M. ; Oxon.B.(B.); P.O.; B.S. 

. [Beports and Transactions] of the American Institute of the City 

of New York. Albany. 
1841 B.M.i.; P.O.i.; B.S.i. 
. American Journal of Mathematics. Baltimore. 

1878 B.M.; Camb.P.S.; Camb.U.; Dub.N.L.I. ; Dub.B.I.A. 
Dub.T.C.; Edinb.B.S.; Edinb.U.; Glasg.U.i.; Math.S.; Oxon.B. 
Oxon.B.; B.A.S.; B.S.; U.C.L. 
.. The American Journal of Science and Arts; Silliman. New Haven 

1818 B.M.; Camb.P.S.i.; Camb.U.; Chem.S.i.; Dub.N.L.I.i. 
Dub.B.C.S.i.; Dub.T.C.i.; Edinb.R.S.; Edinb.U.; Geol.M. 
Glasg.P.S.; Glasg.U.i.; N.H.M.; Oxon.B.; Oxon.R.; P.O. 
R.A.S.i.; B.S. 

See Silliman J. 

.. Proceedings of the American Philosophical Society. Philadelphia. 
1840 Camb.P.S.; Camb.U.i.; Chem.S.i.; Dub.B.I.A.; Edinb 

B.S.; Glasg.P.S.i.; Glasg.U.i.; Linn.S.; Math.S.i.; N.H.M.i. 

Oxon.B.; Oxon.B.i.; P.O.; B.A.S.; R.S.; U.C.L. 
Transactions of the American Philosophical Society. Philadelphia. 
1771 B.M.i.; Camb.P.S.; Camb.U.i.; Chem.S.i.; Dub.R.I.A.; 



List of Serial Publications 



Am. S. CE. T 

Axnst. Alt. Jb 



Amst. Alt. P 



Amst. Alt. Vh 



st. Ak. Vs 



Amst. Alt. Vs. M 



Amst. Ak. Wet. F 



Amst. Arch. Wisk. Gn. 



Amst. Jb 

Amst. Jb. Ak 

Amst. Mengelwerk 



Amst. N. Vb 



Amst. N. Ws. Ntk. Vb. . . 
Amst. Ts. Ws, Nt. Wet. 



Amst. Vb. 

Amst. Vb. Ak. 



Amst. Vs. Ak.. 
A. Mt. 



Edinb.R.S.; Linn.S.; N.H.M.i.; Oxon.B. ; Oxon.R.i. ; P.O.; 

E.A.S.i.; R.S.; U.C.L.i. 

Transactions of the American Society of Civil Engineers. New York. 
1871 P.O. 
Jaarboek van de Koninklijke Akademie van Wetenschappen gevestigd. 

te Amsterdam. Amsterdam. 
1857 B.M.; Camb.P.S.; Dub.B.D.S.; Dub.T.C.; Edinb.R.S.i.; 

Glasg.P.S.i.; Linn.S.; N.H.M.; R.A.S.i.; R.S.; U.C.L.i. 
See Amst. Jb. and Amst. Jb. Ak. 

Koninklijke Akademie van Wetenschappen te Amsterdam. Pro- 
ceedings of the Section of Sciences. Amsterdam. 
1899 Camb.P.S.; Camb.U.; Chem.S.; Dub.R.I.A. ; Dub.T.C.; 

Edinb.R.S.; Glasg.P.S.; Glasg.U.; Oxon.B.; R.A.S.; R.S. 
Verhandelingen der Koninklijke Akademie van Wetenschappen. 

Amsterdam. 
1854 Camb.P.S.; Camb.U.; Dub.N.L.I. ; Dub.R.I.A.i.; Edinb. 

R.S.; Glasg.P.S.i. ; Glasg.U.; Linn.S.; N.H.M. ; Oxon.B.; 

R.A.S.; R.S.; U.C.L.i. 
Verslagen der Zittingen van de Wife- en Natuurkundige Afdeeling der 

Koninklijke Akademie van Wetenschappen. 1893, 1894. 
Verslagen van de Zittingen der Wis- en Natuurkundige Afdeeling 

van de Koninklijke Akademie van Wetenschappen. 1895, 1896. 
Koninklijke Akademie van Wetenschappen te Amsterdam. Verslagen 

van de Gewone Vergaderingen der Wis- en Natuurkundige 

Afdeeling. Amsterdam. 
1897 B.M. ; Camb.P.S.; Camb.U.; Dub.T.C.; Edinb.R.S.; 

Glasg.P.S.; Glasg.U.; N.H.M. ; R.A.S.; R.S. 
Verslagen en Mededeelingen der Koninklijke Akademie van Weten- 
schappen. Afdeeling Natuurkunde. Amsterdam. 
185392. B.M. ; Camb.P.S.; Camb.U.; Dub.T.C.; Edinb.R.S.; 

Glasg.P.S.; Linn.S.; N.H.M.; Oxon.B.i.; R.A.S.i.; R.S.; U.C.L.i. 
See Amst. Vs. Ak. 
Processen-Verbaal van de Gewone Vergaderingen der Koninklijke 

Akademie van Wetenschappen, Afdeeling Natuurkunde. 
186584. Dub.R.D.S.; Linn.S.i.; R.A.S.; R.S. 
Archief uitgegeven door net Wiskundig Genootschap. Amsterdam. 
1856 B.M.; R.S.i.; U.C.L.i. 
See Arch. Wisk. On. 
Het Instituut. Amsterdam. 
184146. B.M. ; Edinb.R.S.i. 

' See Amst. Ak. Jb. 

Mengelwerk van uitgeleezene en andere Wis- en Natuurkundige 
Verhandelingen ; door het Genootschap der Mathematische Weten- 
schappen, etc. Amsterdam. 

17961816. R.S. 

See Mengelwerk Wisk. Vb. 

Nieuwe Verhandelingen der eerste Klasse van het Koninklijk Neder- 
landsche Instituut van Wetenschappen, Letterkunde, en Schoone 
Kunsten te Amsterdam. Amsterdam. 

182752. B.M.; Camb.U.; Dub.T.C.; Edinb.R.S.; Linn.S.; 
N.H.M.; R.S. 

Nieuwe Wis- en Natuurkundige Verhandelingen van het Genootschap 
te Amsterdam. Amsterdam. 

184454. B.M.; R.S. 

Tijdschrift voor de Wis- en Natuurkundige Wetenschappen, Letter- 
kunde, en Schoone Kunsten te Amsterdam. Amsterdam. 

184752. B.M.; Camb.U.; Dub.T.C.; Edinb.R.S.i.; Linn.S.; 
Oxon.B.; R.S. 

\ Verhandelingen der Eerste Klasse van het Koninklijk Nederlandsche 

( Instituut van Wetenschappen, Letterkunde, en Schoone Kunsten 
te Amsterdam. Amsterdam. 

181225. B.M.; Camb.U; Dub.T.C.; Edinb.R.S.; N.H.M.; 
Oxon.B.; R.S. 

See Amst. Ak. Vs. Itt. 

Annali di Matematica pura ed applicata. . . ; Tortolini. Roma, Milano. 

1858 B.M.; Camb.U.i.; Dub.R.D.S.; Dub.T.C.; Edinb.U.; 
Glasg.U.i.; Math.S.i.; Oxon.B.(R.); R.S.; U.C.L. 

See Tortolini A. 

xi 6 



List of Serial Publications 



A. Mth. . 



Amt. Mch. 8. J. 

Angers mm. S. Ag. 
Angers 8. Be. nil. ... 
A. Pon. C haus s 



Arch. f. Ap. 

Arch. Mth. Ntvd. . . 
Arch. Mth. Ps 

Arch. NeerL 

Arch. 8c. Ps. Nt. ... 



Arch. Wisk. On 

Arg. S. Ci. A. ... 



As. & Asps. 



A. Sc. Lomb. Ven. 
A. Sc. Nt. ... 



As. Pr. C. R. 



AshmoL 8. F. 



Annals of Mathematics. University of Virginia. Charlottesville, Va. 
1884 Camb.P.S.; Camb.U.; Dub.B.I.A.i.; Edinb.B.S.; Math.S.i.; 

Oxon.B. 

The [Quarterly] Journal of the Amateur Mechanical Society. London . 
187279. B.M.; P.O. 

M<hnoires de la Societe d'Agriculture, Sciences, et Arts. Angers. 
1831 B.M. ; N.H.M.i.; Oxon.B. i. ; B.S.i. 
Bulletin de la Societe d'Etudes Scientifiques d'Angers. Angers. 
1872 B.M.; N.H.M. 

Annales des Fonts et Chaussees. Memoires et documents relatifs 

a 1'Art des Constructions et au Service de 1'Ingenieur. Paris. 

1831 B.M.; Camb.U.; Edinb.U.i. ; Glasg.P.S.i.; Glasg.U. i.; 

P.O.; R.S.i. 

See Par. A. Pon. Chauss. 

Annalen der Physik und Chemie ; Poggendorff . Leipzig. 
1824 B.M. ; Camb.P.S.i.; Camb.U.; Chem.S.; Dub.R.I.A. ; 
Dub.T.C.; Edinb.E.S.; Edinb.U.; Glasg.P.S.i.; Glasg.U.*.; 
N.H.M. ; Oxon.B. (B.); P.O.; E.S.; U.C.L.i. 
See Pogg. A. 
Archiv fiir Anthropologie. Zeitschrift fiir Naturgeschichte und 

Urgeschichte des Menschen. Braunschweig. 
1867 B.M.; Camb.U.; Dub.N.L.I. ; N.H.M.i.; Oxon.B.; B.S. 
Archiv for Mathematik og Naturvidenskab. Kristiania. 
1876 B.M.; Camb.U.; Dub.B.I.A.i.; Edinb.E.S.; Math.S.i.; 

N.H.M.; Oxon.B.; Oxon.B.i.; B.S. 

Archiv der Mathematik und Physik ; Grunert. Greifswald, Leipzig. 
1841 B.M. ; Camb.U.; Dub.N.L.I.; Dub.B.C.S.; Edinb.U.; 

Glasg.U.; Math.S.i.; Oxon.B.(E.); B.S.; U.C.L.i. 
See Grunert Arch. 
Archives Neerlandaises des Sciences Exactes et Naturelles. La Haye, 

Harlem. 

1866 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.E.I.A. ; 
Dub.T.C.; Edinb.E.S.; Geol.M.i. ; Glasg.P.S.; Glasg.U.; 
Linn.S. ; Math.S.; N.H.M.; Oxon.B.; P.O.; E.S.; U.C.L.i. 
Bibliotheque Universelle. Archives des Sciences Physiques et 

Naturelles. Geneve. 

1846 B.M.; Camb.U.; Chem.S.i.; Dub.N.L.I.i.; Dub.B.D.S.i.; 
Dub.B.I.A.i.; Edinb.E.S.; Edinb.U.; Glasg.U.; N.H.M.; Oxon. 
B.; P.O.; E.S. 
See Bb. Un. Arch. 
See Amst. Arch. Wisk. Gn. 

Anales de la Sociedad Cientifica Argentina. Buenos Aires. 
1876 B.M.i.; N.H.M. 
L'Astronomie. Eevue d'Astronomie populaire, de Me'teorologie et de 

Physique du Globe. Paris. 

188294. B.M.; Camb.U.i.; Edinb.E.S.; E.A.S.; B.S.i. 
Astronomy and Astrophysics. Northfield, Minn. 
189294. B.M.; Camb.P.S.i.; Dub.N.L.I.i.; B.A.S.; B.S. 
Annaes das Sciencias e Lettras, publicados debaixo dos auspicios da 
Academia Eeal das Sciencias; Sciencias mathematicas, physicas, 
historico-naturaes e medicas. Lisboa. 
1857 B.M. ; Dub.E.I.A.; Edinb.E.S.i. ; N.H.M.; E.A.S.i. ; 

E.S.i. 

See Lisb. A. 

Annali delle Scienze del Begno Lombardo-Veneto. Padova e Venezia. 
1831-45. B.M. ; Camb.U.; Dub.T.C.i.; Oxon.B. 
Annales des Sciences Naturelles, comprenant la Physiologic animale 
et vegetale, 1'Anatomie comparee des deux regnes, la Zoologie, la 
Botanique, la Mineralogie et la Geologic. Paris. 
1824 B.M.; Camb.P.S.; Camb.U.; Dub.E.D.S.; Dub.T.C.; 
Geol.M.i.; Glasg.P.S.i. ; Linn.S.; N.H.M.; Oxon.B.; P.O.i.; 
E.S.; U.C.L.i. 
Association Francaise pour 1'Avancement des Sciences. Compte 

Eendu. Paris, etc. 
1872 B.M.; Camb.U.; Edinb.E.S.; Edinb.U.; Geol.M.; Glasg. 

P.S.; Glasg.U.; N.H.M.; P.O.; B.A.S.i.; E.S. 
Abstracts of the Proceedings of the Ashmolean Society. Oxford. 
184481. Camb.U.; Dub.B.D.S. ; Edinb.E.S.i.; N.H.M.; Oxon. 
B.i. ; Oxon.E. ; P.O.i.; B.S. 



List of Serial Publications 



Ashmol. S. T. ... 
As. J. ... 



As. Nr. 



Asps. J 

As. Researches . 

As. S. J 

As. S. Mm. 

As. S. M. Not 

As. S. Pac. Pb 

As. S. T. . 



Assur. Mg 



At. Ac. It.... 
A. Tel. . 



Atlantis 



At. Sc. It 

Aube mm. S. Ag. 



Ausl 

Aust. As. Up. ... 



Barcel. Ac. Bl. 



Barcel. Ac. Mm... 



Transactions of the Ashmolean Society. Oxford. , 

183476. Camb.U. ; Dub.R.D.S. ; Edinb.E.S.; N.H.M.i. ; Oxon 

B.i.; Oxon.E.; P.O.i.; B.S.i. 
The Astronomical Journal. Boston. 
185161. 1888 B.M.; Camb.U.; Glasg.U.*.; Oxon.B.; Oxon.B.i.; 

E.A.S.; R.S.i. 
See Gould As. J. 

Astronomische Nachrichten ; Schumacher. Altona. 
1823 B.M.; Camb.U.; Dub.R.I.A.i. ; Edinb.R.S.; Edinb.U.i.; 

Glasg.U.*.; Oxon.B. (R.) ; E.A.S.; E.S.; U.C.L.i. 
The Astrophysical Journal. Chicago. 
1895 B.M.; Camb.P.S.; Camb.U.; Dub.N.L.I. ; Dub.E.D.S.; 

Glasg.U.; Oxon.E.i.; E.A.S.; U.C.L. 

Asiatick Eesearches ; or Transactions of the [Bengal] Society insti- 
tuted for inquiring into the History and Antiquities, Arts, Sciences, 

and Literature of Asia. Calcutta. 
17881836. B.M.; Camb.U.; Edinb.E.S.i. ; Edinb.U. ; Linn.S.; 

N.H.M.; Oxon.B.; Oxon.E.; E.A.S.; E.S.; U.C.L.i. 
Journal of the Eoyal Asiatic Society. London. 
1834 B.M.; Camb.U.; Dub.E.D.S.; Edinb.E.S.i.; Edinb.U.i.; 

Linn.S.; Oxon.B.; Oxon.E.; P.O.i.; R.A.S.i.; E.S.i.; U.C.L.i. 
Memoirs of the Astronomical Society of London. London. 

1822 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.E.I.A. ; 
Dub.T.C. ; Edinb.E.S. ; Edinb.U. ; Glasg.P.S.i. ; Glasg.U. ; 
Oxon.B.; Oxon.R. ; P.O.i.; E.A.S.; E.S.; U.C.L. 

Monthly Notices of the Astronomical Society of London. London. 
1827 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.E.I.A.; 

Edinb.E.S.; Glasg.P.S.i.; Glasg.U.; Oxon.B. i. ; Oxon.E.i. ; 

P.O.i.; E.A.S.; E.S.; U.C.L. 
Publications of the Astronomical Society of the Pacific. San 

Francisco. 

1889 B.M.; Camb.U.i.; Dub.E.D.S.i.; E.A.S.; E.S.i. 
Transactions of the Eoyal Asiatic Society of Great Britain and 

Ireland. London. 
182735. B.M.; Camb.U.; Dub.E.I.A.; Edinb.E.S.; Edinb.U.; 

Linn.S.; Oxon.B.; Oxon.E.; E.A.S.; E.S.; U.C.L. 
The Assurance Magazine and Journal of the Institute of Actuaries. 

London. 
183067. B.M. ; Camb.U.i.; Edinb.E.S.i.; E.A.S.i. ; E.S.i.; 

U.C.L.i. 

Atti dell' Accademia Italiana di Scienze, etc. Livorno. 
1810. B.M.; Camb.U.; Dub.T.C.; N.H.M.; Oxon.B. 
Annales Telegraphiques, publiees sous le patronage du Directeur 

General des Lignes Telegraphiques. Paris. 
1855 B.M.i.; Camb.U.i.; P.O. 
The Atlantis, or Register of Literature and Science, conducted by 

members of the Catholic University of Ireland. London. 
185863. B.M.; Camb.U.; Dub.N.L.I.; Dub.E.I.A.i.; Edinb.R.S.i.; 

Linn.S.; Oxon.B.; E.S. 

Eiunione degli Scienziati Italian!. Atti. Pisa, etc. 
1839 B.M.; Camb.U.; N.H.M.; E.S. 
M6moires de la Societ6 d' Agriculture, des Sciences, et des Lettres du 

departement de 1'Aube. Troyes. 

1823 B.M.; Camb.U.i.; Dub.T.C. i.; Oxon.B.; E.S.i. 
Das Ausland. Miinchen und Stuttgart. 

182893. B.M.; Camb.U.i.; N.H.M.i.; Oxon.B. i. 

Eeport of the Meeting of the Australasian Association for the 

Advancement of Science. Sydney. 
1888 Camb.P.S.; Camb.U.; Chem.S.; Dub.E.D.S.; Dub.E.I.A.; 

Edinb.E.S.; Edinb.U.i.; Geol.M.; Glasg.U.; Linn.S.i.; N.H.M.; 

Oxon.B.; Oxon.E.; P.O.; E.A.S.; E.S. 

Boletin de la Eeal Academia de Ciencias y Artes de Barcelona. 

Barcelona. 
1892 N.H.M. 
Memorias de la Eeal Academia de Ciencias Naturales y Artes de 

Barcelona. Barcelona. 
[1st Series cannot be traced.] 1876 N.H.M. 

xiii b 2 



List of Serial Publications 



B. A. Bp. .. 



Basel B. 



Basel Vh. .. 



Batav. Wtk. Ts. . 
Baumgartner Z. 

Bb. Brit. 

Bb.lt 

Bb. Mtfc. . 



Bb. TTn 



Bb. Tin. Arch. ... 



Belfast NH. 8. P. 

Belfast NH. 8. Bp. & P. 



Beng. As. 8. J. 



Beng. As. 8. P. 



Beng. J. As. 8.... 
Berg-Hm. Ztg. 



Berg. Ms. Aarb. 



Berl. Ab. 

Berl. Alt. Ab. 



Berl.Ak.BKb 



Report of the Meeting of the British Association for the 

Advancement of Science. London. 

1831 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.B.D.S.; 
Dub.K.I.A.; Dub.T.C.; Edinb.E.S.; Edinb.U.; Geol.M.; Glasg. 
P.S.; Glasg.U.; Linn.S.; N.H.M.; Oxon.B.i.; Oxon.E.; P.O.; 
E.A.S.; E.S.; U.C.L. 

Bericht iiber die Verhandlungen der Naturforschenden Gesellschaft 

in Basel. Basel. 

183552. B.M.; Camb.P.S.; Dub.T.C.; Linn.S.; N.H.M.; E.S. 
Verhandlungen der Naturforsehenden Gesellschaft in Basel. Basel. 
1857 B.M.; Camb.P.S.; Camb.U.; Chem.S. ; Dub.B.D.S.i. ; 

Dub.E.I.A.i.; Dub.T.C.i.; Edinb.E.S.; Linn.S.; N.H.M. ; 

Oxon.E.; E.A.S.i.; E.S.; U.C.L.i. 

Natuurkundig Tijdschrift voor Nederlandsch-Indie. Batavia. 
1850 Camb.P.S.; Camb.U.; Edinb.E.S.i.; Linn.S.; N.H.M. ; 

E.A.S.i.; E.S.i.; U.C.L.i. 
Zeitschrift fiir Physik, Mathematik, undverwandte Wissenschaf ten ; 

Baumgartner und von Ettingshausen. Wien. 
182642. B.M.; Camb.U.i.; Oxon.B.i. (E.) ; E.S.i.; U.C.L.i. 
Bibliotheque Britannique, ou Eecueil extrait des Ouvrages Anglais 

periodiques et autres : partie des Sciences et Arts. Geneve. 
17961815. B.M.; Edinb.U.; N.H.M.; Oxon.B.; P.O.; E.S. 
Biblioteca Italiana, ossia Giornale di Letteratura, Scienze, etc. 

Milano. 

181656. B.M.; Edinb.E.S.i.; Oxon.B. 
Bibliotheca Mathematica. Stockholm and Leipzig. 
1887 B.M.; Camb.U.; Glasg.U.; Oxon.B.; Oxon.E.; E.S. ; 

U.C.L. 
Bibliotheque Universelle des Sciences, Belles-Lettres, et Arts, faisant 

suite a la Bibliotheque Britannique rdigee a Gene've. Partie des 

Sciences. Geneve. 
181645. B.M.; Camb.U.; Dub.E.I.A.i.; Edinb.E.S.i.; Edinb.U.; 

N.H.M.; Oxon.B.; P.O.; E.S. 
Bibliotheque Universelle. Archives des Sciences Physiques et 

Naturelles. Geneve. 
1846 B.M.; Camb.U.; Chem.S.i.; Dub.N.L.I.i. ; Dub.E.D.S. i. ; 

Dub.E.I.A.i.; Edinb.E.S.; Edinb.U.; Glasg.U.; N.H.M.; Oxon.B.; 

P.O.; E.S. 
See Arch. Sc. Ps. Nt. 

(Eeport and Proceedings of the Belfast Natural History and Philo- 
sophical Society. Belfast. 

11852 B.M.i.; Camb.P.S.; Dub.N.L.L; Dub.E.D.S.; Dub.T.C.; 
( Edinb.E.S.i.; Glasg.P.S.i.; N.H.M.; P.O.i.; B.A.S. 
Journal of the Asiatic Society of Bengal. Calcutta. 

1832 B.M.; Camb.P.S.i.; Camb.U.; Dub.E.D.S.; Dub.E.I.A.; 
Dub.T.C.; Edinb.E.S.i.; Linn.S.; N.H.M.; Oxon.B.; Oxon.E.i.; 
E.A.S.i.; E.S.; U.C.L. 

See Beng. J. As. 8. 

Proceedings of the Asiatic Society of Bengal. Calcutta. 

1865 B.M.; Camb.P.S.i.; Camb.U.; Dub.T.C.; Edinb.E.S.i.; 

Edinb.U.i.; Linn.S.; N.H.M.; Oxon.B.; E.A.S.i.; E.S.; U.C.L. 
See Beng. As. 8. J. 
Berg- und hiittenmannische Zeitung; mit besonderer Benicksich- 

tigung der Mineralogie und Geologie; Hartmann. Nordhausen 

und Leipzig. 

1842 B.M.; N.H.M.; P.O. 
Bergens Museums Aarbog for Afhandlinger og Aarsberetning 

udgivne af Bergens Museum. Bergen. 

1892 B.M.; Camb.P.S.; Edinb.E.S.; Linn.S.; N.H.M.; Oxon.E.; 
E.S. 

(Abhandlungen der Koniglichen Akademie der Wissenschaften zu 
Berlin. Berlin. 
1804 B.M.; Camb.P.S.; Camb.U.; Dub.E.D.S.; Edinb.E.S.; 
Edinb.U.; Glasg.U.; Linn.S.i.; N.H.M.; Oxon.B; Oxon.E.; 
P.O.i.; E.A.S.i.; E.S.; U.C.L.i. 
Monatsberichte der K. Preuss. Akademie der Wissenschaften zu 

Berlin. Berlin. 
185681. B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.E.D.S.i.; 



List of Serial Publications 



Berl. B. 



Berl. Mb 

Berl. Mm 

Berl. Mm. Ac 



Berl. Pol. Os. Vli. 
Berl. Ps. Gs. Vh. 
Berl. Sm. D. Ab. .. 



Dub.B.I.A.i.; Dub.T.C.i.; Edinb.B.S.; Glasg.P.S.i.; Glasg.U.i.; 
Linn.S.; Math.S. i.; N.H.M.; Oxon.B.; Oxon.B.; P.O.; B.A.S i.; 
B.S.; U.C.L. 
See Berl. Mb. 

Berl. Ak. Sb Sitzungsberichte der K. Preussischen Akademie der Wissenschaften 

zu Berlin. Berlin. 

1882 B.M. ; Camb.P.S. ; Camb.U.; Chem.S.; Dub.B.D.S.; 
Dub.B.I.A. ; Dub.T.C. ; Edinb.B.S.; Edinb.U.i.; Glasg.P.S. ; 
Glasg.U.; Linn.S.; Math.S.; N.H.M.i.; Oxon.B.; Oxon.B.; 
P.O.; B.A.S.; B.S.; U.C.L. 

Berl. As. Jb Berliner Astronomisches Jahrbuch ; Encke. Berlin. 

1776 Camb.U.; B.A.S. ; B.S.i. 

Berl. B Bericht uber die zur Bekanntmachung geeigneten Verhandlungen 

der K. Preuss. Akademie der Wissenschaften zu Berlin. Berlin. 
183655. B.M.; Dub.B.I.A.i. ; Edinb.B.S.; Linn.S.; N.H.M. ; 

Oxon.B.; P.O.; B.A.S.; B.S. 
. Berichte der Deutschen Chemischen Gesellsehaft. Berlin. 

1868 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.N.L.L; Glasg. 
P.S.; Glasg.U.; N.H.M.; Oxon.B.; P.O.; B.S.; U.C:L.i. 

. See Berl. Ak. Mb. 

,-Memoires de 1' Academic Boyale des Sciences de Berlin. Berlin. 
J 1770 1804. B.M.i.; Camb.U.; Dub.E.D.S.i.; Dub.T.C.i.; Edinb. 
' I B.S.; Edinb.U.; N.H.M.; Oxon.B.; P.O.; B.S.; U.C.L. 

Berl. Pol. Gs. B Bericht iiber die Verhaltnisse und die Wirksamkeit der Polytech- 

nischen Gesellsehaft zu Berlin. Berlin. 
183951. E.S. 
. Verhandlungen der Polytechnischen Gesellsehaft. Berlin. 

1851 B.S.i. 

. Verhandlungen der Physikalischen Gesellsehaft in Berlin. Berlin. 
1882 Camb.P.S. i.; Camb.U.; N.H.M.; Oxon.B.; P.O.; B.A.S.; B.S. 
. Sammlung der Deutschen Abhandlungen, welche in der K. Akademie 
der Wissenschaften zu Berlin vorgelesen worden in den Jahren 
17881803. Berlin. 
17891803. B.M.; N.H.M.; B.S. 

Berl. Z. Erdk Zeitschrift der Gesellsehaft fur Erdkunde zu Berlin; Koner. 

Berlin. 
1866 B.M.; Camb.U.; Dub.B.I.A.i.; N.H.M.; Oxon.B.; B.S.i. 

Bern Mt Mittheilungen der Naturforschenden Gesellsehaft in Bern. Bern. 

1843 B.M.; Camb.P.S.i.; Dub.E.D.S.i. ; Dub.B.I.A.i.; Edinb. 
E.S.i.; N.H.M.; B.S. 

Birm. Ph. s. P Proceedings of the Birmingham Philosophical Society. Birmingham. 

1876 B.M.; Camb.P.S.; Camb.U.; Dub.B.I.A.i.; Dub.T.C. i.; 
Edinb.B.S.; Edinb.U.i.; Geol.M.; Glasg.P.S.; Linn.S.i.; N.H.M.; 
Oxon.B.; Oxon.B.; P.O.; B.A.S. i.; E.S.; U.C.L.i. 

Bll. As Bulletin Astronomique publi6 sous les Auspices de 1'Observatoire de 

Paris. Paris. 

1884 B.M.; Camb.U.; Edinb.B.S.; Oxon.B.; B.A.S. 
Bll. Sc. Mth Bulletin des Sciences Mathematiques. Paris. 

1885 Camb.U.; Dub.T.C.; Edinb.B.S.; Glasg.U.; Math.S.; 
Oxon.B.; Oxon.B.; E.A.S.; B.S.; U.C.L. 

Bll. Sc. Mth. As Bulletin des Sciences Mathematiques et Astronomiques. Paris. 

187084. B.M. ; Camb.U.; Edinb.E.S. ; Math.S.; Oxon.E. ; 
B.A.S.i.; E.S.; U.C.L.i. 

Bll. Sc. Nord Bulletin Scientifique, Historique et Litt6raire du Departement du 

Nord et des pays voisins. Lille. 

1869 Camb.U.; Linn.S.; N.H.M. 

{Astronomisches Jahrbuch, nebst einer Sammlung der neuesten in 
die astronomischen Wissenschaften einschlagenden Abhandlungen, 
Beobachtungen, und Nachrichten ; Bode. Berlin. 
17761829. Dub.T.C.i.; B.A.S.; E.S.i. 

Bohm. Gs. Ab.. 4 Abhandlungen der K. Bohmischen Gesellsehaft der Wissenschaften. 

Prag. 
180492. B.M.i.; Camb.P.S.; Camb.U.i. ; Dub.B.I.A.i.; Edinb. 

E.S.i.; Linn.S.i.; N.H.M.; Oxon.B.; B.S.i. 
See Prag Ab. 

Bohm. Gs. Ws. Jbr Jahresbericht der Konigl. Bohm. Gesellsehaft der Wissenschaften. 

Prag. 
1876 B.M.i.; Edinb.E.S.i.; Linn.S.i.; N.H.M.; B.S. 



Bologna Ac. Mm 

Bologna Ac. Sc. Mm. 

Bologna Km. Ac 

Bologna Dim. Ac. Sc. 

Bologna Mm. I. It. 



Bologna N. A 



Bologna N. Cm 



Bologna Opusc. Sc 

Bologna Opusc. Sc. N. 

CoL 
Bologna Bd 



Bdne Ac. Hip. Bll 

Bonn Niedr. Os. Sb. ... 



Bordeaux Ac. Act 



Bordeaux Ac. Sc. Se. Pbl. 
Bordeaux Ac. Se. Pbl. ... 

Bordeaux Act. Ac. Sc. . . . 
Bordeaux Mm. S. Sc. . . . 
Bordeaux Mm. S. Sc. Ps. 



Bordeaux Obs. A. 



Bordeaux S. Sc. Mm. 
Bordeaux S. Sc. FV. .. 



Bost. Am. Ac. Mm. 



Boat. J. Ph. ... 



Bost. Mm. Am. Ac 

Braunschw. Vr. Nt. Jbr. 



Brem. Ab 



Brescia At. Cm 

Brescia Cm. 



List of Serial Publications 

(Memorie della Accademia delle Scienze dell' Istituto di Bologna. 
Bologna. 
1850 B.M. ; Camb.U. ; Dub.R.I.A.; Edinb.R.S.; N.H.M. ; 
Oxon.B.; R.A.S.; B.S.; U.C.L.i. 
Memorie dell' Istituto Nazionale Italiano : Classe di Fisica e di 

Matematica. Bologna. 
180613. B.M.; Camb.U.; Dub.R.I.A.; Dub.T.C.; Edinb.R.S. i.; 

N.H.M.; Oxon.B.i.; R.S.i. 
Nuovi Annali delle Scienze Naturali; Alessandrini, Bertolini, 

Gherardi, e Ranzani. Bologna. 
1838-54. Camb.U.; N.H.M.; Oxon.B.i.; R.S. 
See if. A. Sc. Nt. 
Novi Commentarii Academies Scientiarum Instituti Bononiensis. 

Bononise. 

183449. Camb.U.; Edinb.R.S.; N.H.M.; Oxon.B.; R.S. 
Opuscoli Scientific!. Bologna. 
181723. B.M.; Camb.U.; Edinb.R.S.i.; N.H.M. 
Nuova collezione d' Opuscoli Scientifici. Bologna. 
182425. Camb.U. 
Rendiconto delle Session! dell' Accademia delle Scienze dell' Istituto 

di Bologna. Bologna. 
1851 B.M.; Camb.U.i.; Dub.T.C.; Edinb.R.S.i.; N.H.M.i.; 

Oxon.B.i.; R.A.S.i.; R.S.i.; U.C.L.i. 
Bulletin de PAcadernie d'Hippone. Bone. 
1865 Camb.U.; N.H.M.i. 
Sitzungsberichte der Niederrheinischen Gesellschaft fur Natur- und 

Heilkunde zu Bonn. Bonn. 

1854 B.M.i.; Camb.U.i.; Edinb.R.S.i.; Linn.S.i.; N.H.M.; 
Oxon.R.; R.S.i. 

Recueil des Actes de PAcademie des Sciences, Belles-lettres, et Arts 
de Bordeaux. Bordeaux. 

1839 B.M.i.; Dub.R.I.A.i.; Dub.T.C.i.; N.H.M.; Oxon.B.i.; R.S.i. 

See Bordeaux Act. Ac. Sc. 

J Seances publiques de PAcademie Royale des Sciences, Belles-lettres, 
/ et Arts de Bordeaux. Bordeaux. 

181937. N.H.M. 

See Bordeaux Ac. Act. 

IMemoires de la Societe des Sciences Physiques et Naturelles de 
/ Bordeaux. Bordeaux. 

1855 Camb.P.S.;Dub.R.D.S.; Dub.T.C.; Edinb.R.S. ;Glasg.P.S.; 
Linn.S.; Math.S.; N.H.M.; Oxon.B.; R.A.S.; R.S. 

See Bordeaux S. Sc. Mm. 

Annales de PObservatoire de Bordeaux. Paris, Bordeaux. 

1885 Dub.R.D.S.; R.A.S.; R.S. 

See Bordeaux Mm. S. Sc. 

Proces-Verbaux des Seances de la Societe" des Sciences Physiques 

et Naturelles de Bordeaux. Paris, Bordeaux. 
1894 Camb.P.S.; Dub.R.D.S.i.; Edinb.R.S.; Math.S.; N.H.M.; 

R.A.S.; R.S. 
Memoirs of the American Academy of Arts and Sciences. Cambridge 

and Boston. 
1785 B.M.i.; Camb.P.S.; Camb.U.; Dub.R.D.S.i.; Dub.R.I.A.i.; 

Dub.T.C.i.; Edinb.R.S.; Linn.S.; N.H.M.; Oxon.R.; P.O.i. ; 

R.A.S.; R.S.; U.C.L.i. 

See Am. Ac. Mm. and Bost. Mm. Am. Ac. 

The Boston Journal of Philosophy and the Arts ; Webster, etc . Boston . 
1824-26. B.M. 

See Am. Ac. Mm. and Bost. Am. Ac. Mm. 
Jahresbericht des Vereins fur Naturwissenschaft zu Braunschweig. 

Braunschweig, Altenburg. 

1879 Dub.R.I.A.i.; Edinb.R.S.; Linn.S.; N.H.M.; R.S. 
Abhandlungen herausgegeben vom Naturwissenschaftlichen Vereine 

zu Bremen. Bremen. 
1868 B.M.; Camb.U.; Dub.R.D.S.i.; Dub.R.I.A.i.; Edinb.R.S.i.; 

Linn.S.; N.H.M.; R.S. 

\Commentarj della Accademia di Scienze, Lettere, ed Arti dell' 
/ Ateneo di Brescia. Brescia. 
1808 B.M.; Camb.U.; N.H.M.i.; Oxon.B.i.; R.S.t. 



List of Serial Publications 



Bresl. SI. Gs. JTbr. 

Brest S. Ac. Bll. . . 
Brugnatelli G 



Eriinn Vll 

Brux. Ac. Bll. 



Brux. Ac. Cent. Anniv. 



Brux. Ac. Mm 

Brux. Ac. Sc. Mm 



Brux. A. Tr. Fbl. 
Brux. A. Un. . . 



Brux. Bll. Ac 

Brux. Mm. Ac. Sc. 
Brux. Mm. Cour. . . . 
Brux. Mm. Cour. 4. 



m. Cour. 8 

Brux. Obs. A. (.!>.) 
Brux. S. As. Bll 



Bucarest Ac. Rom. A. 
Bucarest S. Sc. El... 



Cadiz Period. M. Ci 

Caen Ac. Mm 

Cncs. Leop. Ac. N. Acta. 



Jahresbericht der Schlesischen Gesellschaft fur vaterlandische 

Cultur. Breslau. 

1850 Dub.R.D.S.i.; Dub.R.I.A.i.; N.H.M.; R.S. 
Bulletin de la Societe Academique de Brest. Brest. 
1858 B.M.; Camb.U.i. 
Giornale di Fisica, Chimica, e Storia Naturale ; Brugnatelli, etc. 

Pavia. 
180827. B.M.; Camb.U.; Dub.T.C.; N.H.M.i.; Oxon.B.; P.O.; 

R.S. 

Verhandlungen des Naturforschenden Vereins zu Briinn. Briinn. 
1863 Camb.U. i.; Dub.R.I.A.; Linn.S.; N.H.M.; R.S. 
Bulletins de 1'Academie Royale des Sciences, etc., de Belgique. 

Bruxelles. 
1834 B.M.i. ; Camb.U.; Chem.S.i. ; Dub.R.I.A.; Edinb.R.S. ; 

Glasg.P.S. i.; Glasg.U.i.; Linn.S.; Math.S.i.; N.H.M.; Oxon.B.; 

Oxon.R.; P.O.; R.A.S.; R.S. 
See Brux. Bll. Ac. 
Centieme Anniversaire de Fondation (17721872) de 1'Academie 

Royale de Belgique. Bruxelles. 
1872. B.M.; Camb.U.; Edinb.R.S.; Glasg.P.S.; Linn.S.; N.H.M.; 

P.O.; R.A.S.; R.S. 

} Memoires de 1'Academie Royale des Sciences, des Lettres et des 
j Beaux-Arts de Belgique. Bruxelles. 
1820 B.M.; Camb.P.S.; Camb.U.; Dub.R.I.A.; Dub.T.C.; 

Edinb.R.S.i.; Edinb.U.; Linn.S.i.; N.H.M.; Oxon.B.(R.); P.O.i.; 

R.A.S.i.; R.S. 
See Brux. Mm. Ac. Sc. 

Annales des Travaux Publics de Belgique. Bruxelles. 
1843 B.M.; P.O. 

Annales des Universitds de Belgique. Bruxelles. 
184259. Camb.U.; Oxon.B.; P.O.; R.S.i. 
See Brux. Ac. Bll. 
See Brux. Ac. Sc. Mm. 

) Memoires Couronne"s et Memoires des Savants Etrangers, publ. par 
I 1'Acad. Roy. des Sciences, etc. de Belgique. 4to. Bruxelles. 
1818 B.M.i.; Camb.P.S.; Camb.U.; Dub.T.C.; Edinb.R.S.t.; 

Edinb.U.; Glasg.U.i.; Linn.S.i.; N.H.M.; Oxon.B.; P.O.i.; 

R.A.S.i.; R.S. 
Memoires Couronn6s et autres Memoires, publ. par 1'Acad. Roy. des 

Sciences, etc. de Belgique. 8vo. Bruxelles. 
1840 B.M.; Camb.P.S.; Camb.U.; Dub.T.C.; Edinb.R.S.; 

Glasg.U.i.; Linn.S.i.; N.H.M.; Oxon.B.; P.O.; R.A.S.i.; R.S. 
Annales de 1'Observatoire Royal de Belgique. Bruxelles. 
1834 B.M.; Camb.U.; Dub.R.D.S.; Dub.R.I.A.; Edinb.R.S.; 

Glasg.P.S.i.; Glasg.U.i.; Oxon.B.i.; R.A.S.; R.S.; U.C.L.i. 
Bulletin de la Societe Beige d'Astronomie. Comptes Rendus des 

Seances mensuelles de la Societe et Revue des Sciences d'Obser- 

vation. Astronomie, Meteorologie, Geodesie et Physique du Globe. 

Bruxelles. 
1896 R.A.S. 

Annales de la Societe Scientifique de Bruxelles. Bruxelles. 
1877 B.M.; Dub.N.L.I.i.; Edinb.R.S.; N.H.M. 
Analele Academiei Romane. Bucuresci. 
1880 B.M.; Camb.U.i.; N.H.M.i. 
Buletinul Societatii de Sciinte Fizice (Fizica, Chimia si Mineralogia) 

din Bucuresci-Romania. 
[1892]- [1896]. 
Buletinul Societatii de Sciinte din Bucuresci-Romania. Bucuresci. 

(Bulletin de la Societe des Sciences Bucarest-Roumanie.) 
[1897] Glasg.P.S.; Glasg.U.; N.H.M.; R.S.i.; U.C.L.i. 

Perif'xlico mensual de Ciencias matematicas y fisicas. Cadiz. 

1848. B.M.; R.S. 

Memoires de 1'Academie des Sciences, Arts et Belles-Lettres de 

Caen. Caen. 

1811 B.M.i.; Camb.U.i.; Dub.T.C.i.; N.H.M.i.; Oxon.B.i.; R.S.i. 
Nova Acta physico-medica Academise Cses. Leopoldino-Carolinse 

naturae Curiosorum. Erlangen, Bonn, Breslau. 



Calif. Ac. F. 



Camb. and Dubi. Mth. J. 

Camb. Mm. Anal. 8 

Camb. (M.) Mth. M 

Camb. Mth. J. 

Camb. Ph. S. P. 

Camb. Ph. S. T 



Camb. (U.S.) Mth. M. .. 
Card. Nt. S. T 



Carl Rpm 



Casopis 

Catania Ac. Oioen. At. . 



Catania Ac. Ctioen. Bll. 



Catania At. Ac. Oioen. 
CE. I.F 



Chambery Mm. Ac. Sa\ 

Charleston Md. J. ... 



Chemnitz B 

Cherb. Mm. 8. Ac 

Cherb. Mm. 8. 8c 

Cherb. 8. 8c. Mm 

Cherb. 8. 8c. Nt. Mm. 

Chile A. Un 



List of Serial Publications 

1758 Camb.P.S.; Camb.U.; Chem.S.i.; Dub.T.C.; Edinb.E.S.i.; 
Edinb.U.; Linn.S.i.; Math.S.i.; N.H.M.; Oxon.R.; R.A.S.i.; E.S. 
See Ac. Caes. Leop. N. Acta. 
Proceedings of the California Academy of Natural Sciences. San 

Francisco. 
1854 BJVf.i.; Camb.P.S.i.; Dub.E.I.A.; Edinb.E.S.i.; Glasg.P.S.; 

Linn.S.i.; N.H.M.; P.O.i.; E.S.i. 
The Cambridge and Dublin Mathematical Journal; Thomson and 

Ferrers. Cambridge. 
184654. B.M.; Camb.P.S.i.; Camb.U.; Dub.T.C.i.; Edinb.E.S.; 

Edinb.U.; N.H.M.; Oxon.B.; E.S.; U.C.L. 
Memoirs of the Cambridge Analytical Society. Cambridge. 
1813. B.M.; Camb.U.; Edinb.E.S.; P.O.; E.A.S.; E.S.; U.C.L. 
The Mathematical Monthly; Eunkle. Cambridge (Massachusetts). 
185961. B.M.; Camb.U.; Oxon.B.; P.O.; E.A.S.i.; E.S. ; U.C.L. 
See Camb. (U.S.) Mth. M. 

The Cambridge Mathematical Journal. London. 
183945. B.M. ; Camb.P.S.; Camb.U.; Dub.T.C.; Edinb.U.; 

Glasg.U.; Math.S.i.; Oxon.B.i.; E.S.; U.C.L. 
Proceedings of the Cambridge Philosophical Society. Cambridge. 
1866 B.M.i; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.E.D.S. ; 
Edinb.E.S.; Edinb.U.; Glasg.P.S. i. ; Glasg.U.i.; Linn.S.i.; 
Math.S.i.; N.H.M.; Oxon.B.i.; Oxon.B.i.; P.O.; B.A.S.i.; 
E.S.; U.C.L. 

Transactions of the Cambridge Philosophical Society. Cambridge. 
1822 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.T.C.i. ; 
Edinb.E.S.; Edinb.U.; Glasg.P.S.i. ; Glasg.U.; Linn.S.; Math. 
S.i.; N.H.M.; Oxon.B.; Oxon.E. ; P.O.; E.A.S.; E.S.; U.C.L. 
See Camb. (M.) Mth. M. 

Cardiff Naturalists' Society. Eeports and Transactions. Cardiff. 
1868 B.M.i.; Camb.U.i.; Dub.E.D.S.; Geol.M.i.; Glasg.P.S.i.; 

Linn.S.; N.H.M.; Oxon.B.i.; E.S.i. 
Eepertorium fur physikalische Technik, fur mathematische und 

astronomische Instrumentenkunde ; Carl. Miinchen. 
1865-91. B.M.; Camb.U.i.; Dub.N.L.I.i. ; Oxon.E.; P.O.; E.S. 
See Exner Rpm. 

Casopis pro Pestovani Mathematiky a Fysiky. Prag. 
1872 B.M. 

Atti dell' Accademia Gioenia di Scienze Natural! in Catania. Catania. 
1825 B.M.; Camb.U.i.; Dub.E.I.A.; Edinb.E.S.i.; Linn.S.i.; 

N.H.M.; Oxon.B.; E.S. 
Bulletino mensile della Accademia Gioenia di Scienze Natural! in 

Catania. Catania. 
1888 Dub.E.I.A.; N.H.M.; E.S. 
See Catania Ac. Ctioen. At. 

Minutes of Proceedings of the Institution of Civil Engineers, con- 
taining Abstracts of the Papers and of the Discussions. London. 
1837 B.M.; Camb.P.S.; Camb.U.; Dub.E.C.S.; Dub.E.D.S.; 
Dub.E.I.A.; Edinb.E.S.; Edinb.U.; Glasg.P.S.i.; Glasg.U.; 
Oxon.B.; Oxon.B.i.; P.O.; E.S.; U.C.L. 
See I. CE. P. 

Memoires de la Societe Academique de Savoie. Chambery. 
1825 Camb.U.; Dub.E.I.A.; Dub.T.C.; N.H.M.; Oxon.B.; E.S.i. 
See Sav. Ac. Mm. and Sav. Mm. Ac. 
Charleston Medical Journal and Eeview; Gaillard, de Saussure, etc. 

Charleston. 
184660. B.M. 

Bericht der Naturwiss. Gesellsch. zu Chemnitz. Chemnitz. 
1859 Edinb.E.S.i.; N.H.M.; E.S.i. 

Memoires de la Societe Academique de Cherbourg. Cherbourg. 
1833 B.M.; Camb.U.i.; Edinb.E.S.i.; N.H.M.i.; Oxon.B.i. 

{Memoires de la Societe Imperiale des Sciences Naturelles de Cher- 
bourg. Cherbourg. 
1852 B.M.; Camb.P.S.; Camb.U.; Dub.E.I.A.; Edinb.E.S.i.; 
Linn.S.; N.H.M.; E.A.S.i.; E.S. 
Anales de la Universidad de Chile. Santiago de Chile. 
1843 B.M.i.; Dub.T.C.; N.H.M.i.; Oxon.B.i. 
V,- Santiago de Chile Un. A. 



List of Serial Publications 



Chili S. Sc. Act 



Christiania F 



Christ! ania Skr. (Mth. 
Nt.Kl.) 



Ciel et Terre 



Giving 

C. N 

Cn. I. P 



Cn. J 



Cn. R. 8. P. & T. 



Coimbral. 

Con. des Temps 



Conn. Ac. T. 



Conn. Mm. Ac 



Cornwall Pol. 8. Rp. 
Cornwall Pol. 8. T. 



Cornwall R. I. J. 
C. R. . 



Ore. Ac. Sc. Bll. 



Crelle J 

Crelle J. Mth. ... 



Actes de la Societe Scientifique du Chili (Sociedad cientifica de 

Chile). Santiago. * 
1892 B.M.; Dub.R.D.S.i.; Dub.R.I.A.i.; Edinb.R.S.i.; Linn.S.i.; 

N.H.M.; R.S.i. 
Forhandlinger i Videnskabs-Selskabet i Christiania. Christiania. 

1859 B.M.; Camb.P.S.; Camb.U. ; Dub.R.I.A.; Edinb.R.S.; 
Glasg.P.S.; N.H.M.; Oxon.B.; R.S.; U.C.L.i. 

Skrifter udgivne af Videnskabsselskabet i Christiania. Mathe- 

matisk-Naturvidenskabelig Klasse. Christiania. 
1894 B.M.; Camb.P.S.; Dub.R.I.A.i.; Edinb.R.S.; Glasg.P.S.; 

N.H.M.; Oxon.B.; R.S.; U.C.L.i. 
Ciel et Terre. Revue populaire d'Astronomie, de Me"te"orologie et de 

Physique du Globe. Bruxelles. 
1881 B.M.; Edinb.R.S. i.; R.A.S. 
Der Civilingenieur : Zeitschrift fur das Ingenieunvesen. Freiberg, 

Leipzig. 

1854 B.M.; Camb.U.i.; Dub.R.I.A.i.; P.O. 
The Chemical News and Journal of Physical Science. London. 

1860 Camb.P.S.; Camb.U.i.; Chem.S.; Dub.N.L.I.i.; Dub.R.D.S.i.; 
Dub.R.C.S.i.; Edinb.U.;Geol.M.; Glasg.P.S.; N.H.M.; Oxon.B.i.; 
Oxon.R.; P.O.; R.S.; U.C.L.i. 

Proceedings of the Canadian Institute, Toronto. Toronto. 
187990; 1897 B.M.; Camb.P.S.i.; Dub.R.D.S.; Edinb.R.S.i.; 

Edinb.U.; Glasg.P.S.; Math.S.i.; N.H.M.; Oxon.B.; P.O.; R.A.S.i.; 

R.S. 

Transactions of the Canadian Institute. Toronto. 
1889 B.M.; Camb.P.S.; Dub.R.D.S.; Edinb.R.S.; Edinb.U.; 

Glasg.P.S.; Linn.S.; Math.S.i.; N.H.M.; P.O.; R.A.S. ; R.S. 
The Canadian Journal of Industry, Science, and Art. Toronto. 
1853-78. B.M.i.; Dub.R.I.A.; Edinb.R.S.; N.H.M.; P.O.; 

R.A.S.i.; R.S. 
Proceedings and Transactions of the Royal Society of Canada. 

Montreal. 
1883 Camb.P.S.; Camb.U.; Chem.S.; Dub.R.D.S.i.; Dub.R.I.A.i.; 

Dub.T.C.i.; Edinb.R.S.; Geol.M.i.; Glasg.P.S.; Linn.S.; N.H.M.; 

Oxon.B.; Oxon.R.; P.O.; R.A.S.; R.S.; U.C.L. 
Institute, jornal scientifico e litterario ; Forjaz. Coimbra. 
1853 B.M. 
Connaissance des Temps, a 1'usage des Astronomes et des Navigateurs. 

Paris. 

1679 B.M.i.; Camb.U.; Dub.T.C.; Oxon.B.; R.A.S.i.; R.S. 
Transactions of the Connecticut Academy of Arts and Sciences. 

New Haven. 
1866 B.M.; Camb.P.S.; Camb.U.; Dub.R.I.A.; Edinb.R.S.; 

Glasg.P.S.; Linn.S.; Math.S.i.; N.H.M.; Oxon.R.; P.O.; R.A.S.; 

R.S. 

Memoirs of the Connecticut Academy of Arts and Sciences. New Haven. 
181016. Linn.S.i.; N.H.M.i.; R.S. 

^Reports and Transactions of the Royal Polytechnic Society of 
| Cornwall. Falmouth. 
1833 B.M.; Camb.U.i.; Dub.R.D.S.; Edinb.R.S.i.; Glasg.P.S.i.; 

Glasg.U.i.; Linn.S.; N.H.M.; Oxon.B.i.; P.O.; R.S.; U.C.L.i. 
Journal of the Royal Institution of Cornwall. Truro. 
1864 B.M.; Camb.U.i.; Dub.R.D.S.; Edinb.R.S.; Glasg.P.S.i.; 

N.H.M.; Oxon.B.i.; P.O.; R.A.S.i.; R.S.i.; U.C.L.i. 
Comptes Rendus hebdomadaires des Stances de l'Acade"mie des 

Sciences. Paris. 
1835 B.M. ; Camb.P.S.; Camb.U.; Chem.S.; Dub.R.D.S.; 

Edinb.R.S.i.; Edinb.U.; Geol.M.i.; Glasg.P.S.i.; Linn.S.; N.H.M.; 

Oxon.B.; Oxon.R.i.; P.O.; R.A.S.; R.S.; U.C.L. 
Bulletin International de 1'Academie des Sciences de Cracovie. 

Cracovie. 
1889 B.M.; Camb.U.; Chem.S.; Dub.R.I.A.i.; Edinb.R.S.; 

Glasg.U.; N.H.M.; Oxon.B.; Oxon.R.i.; R.A.S.i.; R.S.; U.C.L.i. 

Journal fur die reine und angewandte Mathematik ; Crelle. Berlin. 

1826 B.M.; Camb.U.; Dub.N.L.I. ; Dub.T.C.; Edinb.R.S.; 
Edinb.U.; Glasg.U.; Math.S.i.; Oxon.B.(R.); R.S.; U.C.L. 



C. B. J 



Cuyper Rv . Un . . . . 



Citg.0pt. 

D. Alpvr. Z 

Danzig N. Schr. 

Danzig Schr 

Delft EC. Pol. A. 
Des Moines Anal. 
Devon. As. T 

D. Gs. Ostas. Mt. 



Dijon Ac. Mm 

Dijon Ac. Sc. Mm. 
Dijon Dim. Ac. ... 

Dijon Ac. Se 

Dijon Be. Ac 

Dingier ... 



D. Mth. Vr. Jbr. 



D. Nf. B. . . 



D. Nf. Tbl. ... 
D. Nf. Vh 



D. Nf. Vsm. B 

Dn. Vcl. Selsk. Skr . 



List of Serial Publications 

The Quarterly Journal of the Chemical Society of London. London. 
1849 B.M. ; Camb.P.S. ; Camb.U.; Chem.S.; Dub.E.C.S.; 

DubBDS.; Dub.B.I.A. ; Dub.T.C.; Edinb.E.S.; Geol.M.i.; 

Glasg.P.S. ; N.H.M.i. ; Oxon.B. ; Oxon.E.i. ; P.O. ; B.S. ; 

U.C.L. 
Revue Universelle des Mines, de la Metallurgie, des Travaux Publics, 

des Sciences, et des Arts, appliques a 1'Industrie; de Cuyper. 

Paris et Liege. 
1857 B.M.; Camb.U.; Dub.B.I.A.i.; Glasg.P.S.i.; Glasg.U.i.; 

N.H.M.; P.O. 
See v. Un. Mines. 

Central-Zeitung fur Optik und Mechanik. Leipzig. 
1880 Edinb.U.i.; P.O.i.; B.S.i. 

Zeitschrift des Deutschen [und des Oesterreichischen] Alpenvereins. 

Miinchen. 

1870 B.M.; Camb.U.; Oxon.B. 
Neueste Schriften der Naturforschenden Gesellschaft in Danzig. 

Danzig. 

182062. B.M.i.; Dub.E.I.A.i.; N.H.M.; Oxon.B.; B.S. 
Schriften der Naturforschenden Gesellschaft in Danzig. Danzig. 
1863 Camb.P.S.; Camb.U.i.; Dub.B.D.S.i. ; Dub.B.I.A.i.; 

Edinb.B.S.i.; Linn.S.i.; N.H.M.; Oxon.B.i.; B.S. 
Annales de 1'Ecole Polytechnique de Delft. Leide. 
188597. Camb.P.S.; Camb.U.; Chem.S.i.; Dub.B.D.S.; Dub. 

B.I. A.; Edinb.B.S.; Math.S.; B.A.S.; B.S. 
The Analyst : a monthly Journal of Pure and Applied Mathematics. 

Des Moines, Iowa. 

187483. Camb.U.; Edinb.B.S.; B.S. 
Beports and Transactions of the Devonshire Association for the 

Advancement of Science, Literature, and Art. Plymouth and 

London. 
1862 Camb.U.;.; Geol.M.; Linn.S.; N.H.M.; Oxon.B.; Oxon. 

B.i.; P.O.; B.S. 
Mittheilungen der Deutschen Gesellschaft fur Natur- und Volkerkunde 

Ostasiens. Yokohama. 
1873 B.M.; Edinb.B.S.i. 

{M4moires de 1'Academie des Sciences, Arts, et Belles-lettres de 
Dijon. Dijon. 
1769 B.M.i.; Camb.U.; Dub.B.D.S.i.; Dub.B.I.A.i.; Dub.T.C.i.; 
Edinb.B.S. i.; N.H.M.; Oxon.B.i.; B.A.S.; E.S.i. 
(Seances publiques de 1'Academie des Sciences, Arts, et Belles-lettres 
\ de Dijon. Dijon. 
(181029. B.M.i.; N.H.M. 
Polytechnisches Journal ; Dingier. Stuttgart. 

1820 B.M.; Camb.U.; Chem.S.i.; Dub.N.L.I.i.; Dub.B.C.S.i.; 
Dub.B.D.S.i.; Edinb.B.S.; Glasg.P.S.i. ; Glasg.U.i.; P.O.; 
B.S.i. 
Jahresbericht der deutschen Mathematiker-Vereinigung. Berlin, 

Leipzig. 
1890 Camb.U.; Dub.B.I.A.; Edinb.B.S.i.; Math.S.i.; Oxon.B.; 

B.S. 
Bericht tiber die Versammlung der Deutschen Naturforscher und 

Aerzte. 
182283. Irregular, see Tageblatt. Camb.U.i.; N.H.M.i.; Oxon. 

B.i.; B.S.i. 
See D. Nf. Vsm. B. 

Tageblatt der... Versammlung Deutscher Naturforscher und Aerzte. 
1836 Irregular, see Ber. and Verh. Camb.U. ; N.H.M. ; Oxon. 

R.f . 
Verhandlungen der Gesellschaft Deutscher Naturforscher und Aerzte. 

Leipzig. 

1890 Camb.U.; N.H.M.; Oxon.B. 
See D. Nf. B. 

DetKongeligeDanske Videnskabernes Selskabs Skrivter. Kiobenhavn. 
180118. B.M.; Camb.P.S.i.; Camb.U.; Edinb.B.S.; N.H.M.; 

Oxon.B.; B.S. 
See Xiob. Dn. Vd. Selsk. Skr. 



List of Serial Publications 



Dorpat Sb 

Douai Mm. S. Ag. ... 

Doubs S. Mm. . 



Dresden Isis Sb 

Dresden Sb. Isis 

Dubl. Ph. J. . 



Dubl. R. S. J. 



Dubl. S. Sc. P 



Dubl. S. Sc. T 



Dunkerque Mm. S. 
cour. ... 



Sitzungsberichte der Naturforscher-Gesellschaft zu Dorpat. Dorpat. 
1861 Dub.R.I.A.i.; Edinb.R.S. i.; Geol.S.; N.H.M.; R.S.i. 
Memoires de la Societe d' Agriculture, de Sciences, et d'Arts, seant 

a Douai. Douai. 

1826 B.M.; Camb.U.i.; Oxon.B.i.; R.S.i. 
Memoires et Comptes Rendus de la Socle" te [Libre] d' Emulation 

du Doubs. Besancon. 
1841 B.M.; N.H.M.i. 
Sitzungsberichte der Naturwissenschaftlichen Gesellschaft Isis in 

Dresden. Dresden. 

1861 Camb.U.i.; Dub.T.C.; Geol.S.; N.H.M. 
The Dublin Philosophical Journal and Scientific Review. Dublin. 
182526. B.M.; Dub.R.D.S.; Dub.T.C.; Edinb.R.S. i.; N.H.M.; 
Oxon.B.; Oxon.R.; R.S.i. 
Journal of the Royal Dublin Society. Dublin. 
185675. B.M.;" Camb.P.S.; Camb.U.; Chem.S.i.; Dub.N.L.I.; 

Dub.R.C.S.; Dub.R.D.S.; Dub.R.I.A. ; Geol.M. ; Glasg.U.i.; 

Linn.S.; N.H.M.; Oxon.B.; Oxon.R.i.; P.O.; R.A.S.; R.S. 
The Scientific Proceedings of the Royal Dublin Society. Dublin. 
1877 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.N.L.I.; Dub. 

R.C.S.; Dub.R.D.S.; Dub.R.I.A.; Edinb.R.S.; Geol.M.; Glasg. 

P.S. ; Linn.S.; Math.S.i. ; N.H.M. ; Oxon.B.; Oxon.R.; P.O.; 

R.A.S.; R.S.; U.C.L.i. 

The Scientific Transactions of the Royal Dublin Society. Dublin. 
1877 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.N.L.I.; Dub. 

R.C.S.; Dub.R.D.S.; Dub.R.I.A.; Dub.T.C.; Edinb.R.S.; Geol.M.; 

Glasg.P.S.; Linn.S.; Math.S.; N.H.M.; Oxon.B.; Oxon.R,; P.O.; 

R.A.S.; R.S.; U.C.L.i. 
Memoires de la Societe Dunkerquoise pour 1 'Encouragement des 

Sciences, des Lettres, et des Arts. Dunkerque. 
1853 B.M.; Oxon.B.; R.S.i. 



Edinb. J. Sc. 



Edinb. Mth. B. P. 



Edinb. W. Ph. J. ... 



. Ph. J 



Edinb. P. B. S. 
Edinb. R. S. P.. 



Edinb. R. S. T 



Edinb. Sc. S. Arts T.. 



The Edinburgh Journal of Science, exhibiting a view of the progress 

of discovery in Natural Philosophy, Chemistry, Mineralogy, 

Geology, Botany, etc. ; David Brewster. Edinburgh. 
18241832. B.M.; Camb.U.; Dub.T.C.; Edinb.R.S.; Edinb.U.; 

Glasg.P.S.;.; Glasg.U.; N.H.M.; Oxon.B.i.; Oxon.R.; P.O.; R.S. 
Proceedings of the Edinburgh Mathematical Society. London and 

Edinburgh. 
1883 B.M.; Camb.P.S.; Camb.U.; Edinb.R.S.; Edinb.U.; 

Glasg.U.; Math.S.; R.S.i. 
The Edinburgh New Philosophical Journal, exhibiting a view of the 

progressive Improvements, etc. in the Sciences, etc. ; Robert 

Jameson. Edinburgh. 
182664. B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.T.C.i.; 

Edinb.R.S.; Edinb.U.; Glasg.P.S.; Linn.S. i.; N.H.M.; Oxon.B.; 

Oxon.R.; P.O.; R.A.S.i.; R.S. 
The Edinburgh Philosophical Journal, exhibiting a view of the 

Progress of Discovery in Natural Philosophy, etc.; David Brewster 

and Robert Jameson. Edinburgh. 
181926. B.M. ; Camb.P.S.; Camb.U.; Chem.S.; Dub.T.C. 

Edinb.R.S.; Edinb.U.; Glasg.P.S.; Linn.S.; N.H.M.; Oxon.B.i. 

Oxon.R.; P.O.; R.A.S.; R.S.; U.C.L.i. 
^ Proceedings of the Royal Society of Edinburgh. Edinburgh. 
(1845 B.M.i.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.N.L.I. 

Edinb.R.S.; Edinb.U.; Geol.M.i.; Glasg.P.S.; Linn.S.; Math.S.i. 

N.H.M.; Oxon.B.i.; Oxon.R.; P.O.i.; R.A.S.; R.S.; U.C.L.i. 
Transactions of the Royal Society of Edinburgh. Edinburgh. 
1788 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.N.L.I.; Dub 

R.I.A.; Edinb.R.S.; Edinb.U.; Geol.M.i.; Glasg.P.S.; Glasg.U. 

Linn.S.; Math.S.i.; N.H.M.; Oxon.B.i.; Oxon.R.; P.O.i.; R.A.S. 

R.S.; U.C.L. 
See Edinb. T. R. S. 

Transactions of the Royal Scottish Society of Arts. Edinburgh. 
1841 B.M.i.; Camb.U.; Dub.R.D.S.; Edinb.R.S.; Edinb.U.; 

Glasg.P.S.; Glasg.U.; P.O.; R.S. 
See Edinb. T. Sc. S. Arts awl 8. Sc. Arts T. 



List of Serial Publications 



Edinb. T. R. S 

Edinb. T. Be. 8. Arts.. 



Elect. 



Elektech. Z 

Eng. 8. T 



Ens. With. 

Epinal (VOW.) A. 
J. Pr. C. . 



Erfurt Ak. Jb. .. 
Erfurt N. Acta 



Erlang. Ps. Bid. 8. Sb. 
Erlang. Sb. Ps. Bid. 8. 



Erman Arch. RB. 
Euro J. d'Ag. ... 



Eure S. As- Rec. 
Evk. . 



Ferussac B1L Sc. With. . 

Finist. S. Sc. Bll. 

Firenzc Ac. Georg. At. . 
Firenze At. Ac. Geory. . 
Firenze Opusc. Sc 

Pbrster AL Bauztg 

Franklin I. J. ... 



See Edinb. R. S. T. 

See Edinb. Sc. 8. Arts T. and Sc. S. Arts T. 

The Educational Times, and Journal of the College of Preceptors. 

London. 
1847 B.M. ; Camb.P.S.i.; Camb.U.i. ; Dub.N.L.L; Math.S.i.; 

Oxon.B.i.; Oxon.B.i.; B.S.i. 
The Electrician. London. 
1862 B.M.i.; Camb.P.S.i.; Camb.U.i.; Dub.N.L.I.i. ; Dub. 

E.C.S.i. ; Edinb.E.S.i. ; Edinb.U.i. ; Glasg.P.S.i.; Glasg.U.i. ; 

Oxon.B.i.; Oxon.E.i.; P.O.; E.S.i.; U.C.L.i. 
Elektrotechnische Zeitschrift. Berlin, Miinchen. 
1880 B.M.; Glasg.U.; P.O. 
Transactions of the Society of Engineers. London. 
1860 B.M.; Camb.U.; Dub.N.L.L; Dub.E.C.S.; Glasg.P.S.i.; 

Oxon.B.; P.O.; E.S.i. 

L'Enseignement Math6matique. Eevue Internationale. Paris. 
1899 Math.S. 

Annales de la Societe d ' Emulation du departement des Vosges. Epinal. 
1831 B.M.; E.S.i. 

Journal fur praktische Chemie ; Erdman, etc. deipzig. 
1834 B.M.; Camb.U.; Chem.S.; Dub.N.L.I.i.; Dub.E.C.S.i.; 

Dub.E.D.S.i.; N.H.M.; Oxon.B.; Oxon.B.; E.S.; U.C.L.i. 
Jahrbucher der koniglichen Akademie gemeinniitziger Wissen- 

schaften zu Erfurt. Erfurt. 
I860 B.M.; N.H.M. 
Nova Acta Academies Electoralis Moguntinse Scientiarum utilium 

quss Erfurti est. Erfurti. 

17991809. B.M.i.; Camb.U.; N.H.M.; Oxon.B.i.; E.S. 
(Sitzungsberichte der Physikalisch-Medicinischen Societat zu Er- 
/ langen. Erlangen. 
1864 B.M.; Camb.P.S.; Dub.E.D.S.; Edinb.E.S.i.; Glasg.U.i.; 

Linn.S.i.; Math.S.i.; N.H.M.; E.S.i. 

Archiv fur wissenschaftliche Kunde von Eussland; Erman. Berlin. 
184167. B.M.; Camb.U.; N.H.M.; Oxon.B.; E.S.i. 
Journal d'Agriculture, de Medecine et des Sciences accessoires. 

Evreux. 

1824-29. B.M.; E.S. 
Eecueil de la Societe d'Agriculture, Sciences, Arts, et Belles-lettres 

du departement de 1'Eure. Evreux. 
183039. B.M.; Camb.U.; Oxon.B.; E.S. 
Eecueil des Travaux de la Socit Libre d'Agriculture, des Sciences, 

des Arts et des Belles-Lettres du departement de 1'Eure. Evreux. 
1841 B.M.; Camb.U.; E.S. 
See Eure Bee. 8. Ag. 
A'Magyar Tud6s Tarsasag' Evkonyvei. Pest. Continued as: 

A'Magyar Tudomanyos Akademia Evkonyvei. Buda. 
183389. B.M.; Edinb.E.S.i.; N.H.M.; Oxon.B.; E.A.S.i.; E.S.; 

U.C.L.i. 

Eepertorium der Physik; Exner. Miinchen, Leipzig. 
186591. B.M.; Camb.U.i.; Dub.N.L.I.i.; Edinb. U.; Oxon.E.; 

P.O.; E.S. 
See Carl Bpm. 

Bulletin des Sciences Mathematiques, Astronomiques, Physiques, et 
Chimiques ; Baron de Ferussac. Paris. 

182431. B.M.; Edinb.U.i.; Oxon.E.; P.O.; U.C.L. 

Bulletin de la Societe d'Etudes Scientifiques du Finistere. Morlaix. 

1879 N.H.M. 

\Atti della E. Accademia economico-agraria dei Georgofili. Firenze. 
(1818 Camb.U.; Dub.T.C.i.; Edinb.E.S.i.; Oxon.B. 

Collezione d' Opuscoli scientifici, etc. Firenze. 

180718. B.M.; N.H.M. 

Allgemeine Bauzeitung ; Forster. Wien. 

1836 B.M.; Camb.U.; P.O. 

Journal of the Franklin Institute of the State of Pennsylvania. 
Philadelphia. 

1828 B.M.; Camb.U.; Chem.S.i. ; Dub.E.I.A. ; Glasg.P.S.i.; 
Oxon.B.; P.O.; E.A.S.i.; E.S.; U.C.L.i. 



List of Serial Publications 



Fr. Cg. Md. Cliir Congres Medico-Chirurgical de France. Paris. 

1863 B.M. 

Fr. Cg. Sc. Sessions des Congres Scientifiques de France. 

183379. B.M.; Camb.U.; N.H.M. 

Freiburg B Berichte iiber die Verhandlungen der Naturf orschenden Gesellschaf t 

zu Freiburg i. B. Freiburg i. B. 

1855 B.M. ; Camb.U.i. ; Dub.R.I.A. ; Linn.S.i. ; N.H.M. ; 
Oxon.E. ; B.S. 

Fr. s. Ag. Mm Memoires d' Agriculture, d'Economie rurale et domestique publics 

par la Society d' Agriculture. Paris. 
1801 B.M.; Edinb.B.S.i.; Oxon.B. 

Fr. 8. Mn. Bll Bulletin de la Societe Mineralogique de France. Meulan, Paris. 

1878 B.M.; Dub.T.C.; Geol.M.; N.H.M.; Oxon.E.; E.S. 

Fschr. Mth Jahrbuch iiber die Fortschritte der Mathematik. Berlin. 

1868 B.M.; Camb.U.; Dub.N.L.L; Dub.E.C.S.; Edinb.U. ; 
Glasg.P.S.i.; Glasg.U.; Math.S.; Oxon.E.; E.S.; U.C.L. 

Fschr. Fs Die Fortschritte der Physik. Berlin. 

1845 Camb.P.S.; Camb.U.; Chem.S.; Dub.N.L.I.i.; Dub.B.I.A.i.; 
Edinb.B.S.i.; Edinb.U.; Glasg.U.; Oxon.B.(E.); P.O.; B.A.S.i.; 
E.S.; U.C.L. 



Gand. A. Ac 

G. Arcad 

Card Apercu Tr 



Card Mm. Ac. 



Gard Not. Tr. Ac., 
Gard Tr. Ac. {' 
Gen. I. Nt. Mm 

Gen. Mm. S. Fs. ... 



Geneva Mm. Ac. 

Geneva Mm. I. Ligure 
Geneva TTn. At 

Gen. a. Ps. Mm 

Gergonne A. Mth 



Gg. S. J 



Gg. S. F. 



Giaxnb. Vico. 



Giessen Oberh. Gs. B. 



Annales Academiae Gandavensis. Gandavi. (Ghent.) 

181931. B.M.; Camb.U.; N.H.M.; Oxon.B. 

Giornale Arcadico di Scienze, etc. Eoma. 

1819 B.M.; N.H.M.i.; Oxon.B. 

Notice [ou Apercu analytique] des Travaux de I'Acade'mie Eoyale du 

Gard. Nimes. 

1807? B.M.; Camb.U.; Oxon.B. 
See Gard Not. Tr. Ac. and Gard Tr. Ac. 
Memoires de 1'Academie du Gard. Nimes. 
1832 B.M.; Camb.U.; Oxon.B.; E.S.i. 

See Gard Apercu Tr. 

Memoires de 1'Institut National Genevois. Geneve. 

1854 B.M.; Camb.U.; Dub.E.D.S.; N.H.M.i.; Oxon.B.; E.S. 

Memoires de la Societe de Physique et d'Histoire Naturelle de 

Geneve. Geneve. 
1821 B.M. ; Camb.P.S.; Camb.U.; Dub.E.I.A.; Dub.T.C.; 

Edinb.E.S.; Glasg.U.i.; Linn.S.; N.H.M.; Oxon.B.; Oxon.E.i.; 

B.A.S.i.; E.S.; U.C.L.i. 
See Gen. S. Ps. Mm. 

Memorie dell' Accademia Imperiale delle Scienze di Geneva. Geneva. 
180914. Camb.U.i.; N.H.M.i.; E.S. 
Memorie dell' Istituto Ligure. Geneva. 
1806. B.M.; Camb.U.; E.S. 
Atti della E. Universita di Genova. Geneva. 
1869 B.M.; Camb.U.; N.H.M. 
See Gen. Mm. 8. Fs. 
Annales de Mathematiques, pures et appliquees; Gergonne. Nimes 

et Paris. 
181031. B'.M.; Dub.T.C.; Edinb.U.i.; Glasg.U.; Oxon.B.(E.); 

E.A.S.i.; E.S.; U.C.L. 

Journal of the Eoyal Geographical Society of London. London. 
183280. B.M.; Camb.P.S.i.; Camb.U.; Dub.E.D.S.; Dub.E.I.A.; 

Edinb.E.S.; Edinb.U.; Geol.M.; Glasg.P.S.; Glasg.U.; Linn.S.; 

N.H.M.; Oxon.B.; Oxon.E.; P.O.; E.S. 

Proceedings of the Eoyal Geographical Society of London. London. 
185792. Camb.P.S. i.; Camb.U.; Dub.T.C.; Edinb.E.S.; Geol.M.; 

Glasg.P.S.i.; Glasg.U.; Linn.S.; N.H.M.; Oxon.B.; Oxon.E.; 

P.O.i.; E.A.S.i.; E.S. 

II Giambattista-Vico, giornale scientifico. Napoli. 
1857. N.H.M.; Oxon.B.i. 
See II Giamb. Vico. 
Berichte der Oberhessischen Gesellschaft fur Natur- und Heilkunde. 

1847 B.M.i.; Camb.P.S.; Dub.E.D.S.i.; Dub.E.I.A.i. ; Edinb. 
E.S.i.; Glasg.P.S.i.; Linn.S.i.; N.H.M.; P.O.i.; B.S.i. 

xxiii 



List of Serial Publications 



Gilbert A. 

Qill Tech. Rep. 
Glasg. I. Eng. T. 

Olasg. P. Ph. B. 
Glasg. Ph. S. P. 

Gleanings Be. . . . 
Ol. Mg 

OL B. QJ. 

G. Mt. 

Gorl. Ab 

Goteb. Hndl. 

Gott. Ab 

Gbtt. Cm. .. 



Gott. Nr. 



Oott. Stud 

Gould As. J 

'8 Gravcnh. I. Ing. Ts. . . . 

Grenoble Ac. Delph. Bll. 

Gr oningcn A. Ac 

Gruitliuisen N. Analekt. 



Gruncrt Arch.. 



Annalen der Physik ; Gilbert. Halle und Leipzig. 

17991824. Camb.U.; Chem.S.; Edinb.U.; N.H.M.; Oxon.B.(E.); 

P.O.; R.S. 

The Technical Repository; Gill. London. 

182227. B.M.; Camb.U.; Edinb.R.S.i.; Oxon.B.; P.O.; R.S.i. 
Transactions of the Institution of Engineers [and Shipbuiders] in 

Scotland. Glasgow. 
1857 Camb.U.i.; P.O.; U.C.L.i. , 

Proceedings of the Philosophical Society of Glasgow. Glasgow. 
1841 B.M.; Camb.P.S.; Camb.U.; Dub.R.D.S.; Dub.R.I.A.; 

Edinb.R.S.; Geol.M.i.; Glasg.P.S.; Glasg.U.i.; N.H.M.; Oxon.B.; 

P.O.i.; R.A.S.; R.S. 
Gleanings in Science. Calcutta. 
182931. B.M.; Edinb.R.S.i.; N.H.M.; U.C.L.t. 
The Geological Magazine or Monthly Journal of Geology. London. 
1864 B.M.; Camb.U.; Dub.N.L.I.; Dub.R.C.S.; Geol.M. ; 

Glasg.P.S.; Glasg.U.; Linn.S.; N.H.M.; Oxon.R.; P.O.i.; U.C.L. 
The Quarterly Journal of the Geological Society of London. London. 
1845 B.M. ; Camb.P.S.; Camb.U.; Chem.S.i. ; Dub.N.L.I.; 

Geol.M.; Glasg.U.; Linn.S.; N.H.M.; Oxon.B.; Oxon.R.; P.O.; 

R.A.S.; R.S.; U.C.L. 
Giornale di Matematiche ad uso degli Student! delle Universita 

Italiane; Battaglini. Napoli. 
1863 B.M.; Camb.U.; Dub.R.C.S.i.; Dub.R.I.A.i.; Math.S.i.; 

Oxon.B.; R.S.; U.C.L.i. 

Abhandlungen der Naturf orschenden Gesellschaf t zu Gorlitz . Gorlitz . 
1827 B.M.; Camb.U.i.; Dub.R.D.S.i.; Dub.R.I.A.i.; N.H.M.; 

R.S. 
Goteborgs Kongl. Vetenskaps och Vitterhets Samhalles Handlingar. 

Goteborg. 
1850 B.M.; Camb.P.S. i.; Dub.R.D.S.i.; Dub.R.I.A.i.; Edinb. 

R.S.i.; N.H.M.; R.S.i. 

Abhandlungen der k. Gesellschaf t der Wissenschaften. Gottingen. 
1843 B.M.; Camb.P.S.; Camb.U.; Dub.R.I.A.; Edinb.R.S.i.; 

Glasg.U.; Linn.S.; N.H.M.; Oxon.B.; Oxon.R.; R.S.; U.C.L.i. 
Commentationes Societatis Regise Scientiarum GSttingensis. Got- 

tingae. 
17781808. B.M.i.; Camb.U.; Dub.R.I.A.i.; Edinb.R.S.; Glasg. 

U.i.; N.H.M.; Oxon.B.; R.S.; U.C.L. 
Commentationes recentiores Societatis, etc. Gottingse. 
180837. B.M.; Camb.U.; Edinb.R.S.i.; N.H.M. ; Oxon.B.; 

Oxon.R.; R.A.S.i.; R.S.; U.C.L. 
Nachrichten von der k. Gesellschaf t der Wissenschaften und der 

Georg-Augusts-Universitat zu Gottingen. Gottingen. 

1845 B.M.; Camb.P.S.; Camb.U.i.; Dub.R.D.S.i.; Dub.R.I.A.i.; 
Dub.T.C.i.; Edinb.R.S.; Glasg.U.; Linn.S.; Math.S.i.; N.H.M.; 
Oxon.B.; Oxon.R.; R.A.S.i.; R.S. 

Gottinger Studien ; Krische. Gottingen. 

184547. N.H.M. ; Oxon.B.i.; R.S.i. 

The Astronomical Journal ; Gould. Cambridge, Mass. 

185161. B.M.; Camb.U.; Glasg.U. i.; Oxon.B.; Oxon.R. i. ; 

R.A.S.; R.S. 
.See AS. J. 
Tijdschrift van het Koninklijk Instituut van Ingenieurs. 's Graven- 

hage. 

1869 B.M. 
Bulletin de PAcademie Delphinale, ou Soci6te des Sciences et Arts 

de Grenoble. Grenoble. 

1846 B.M.; Camb.U.i.; Oxon.B.; R.S.i. 
Annales Academies Groninganae. Groningse. 
181537. B.M.i.; Camb.U.; Dub.T.C.; Oxon.B.; R.S. 

Neue Analekten fur Erd- und Himmelskunde. Gruithuisen. 

Miinchen. 

183236. B.M.; R.A.S.; R.S. 

Archiv der Mathematik und Physik ; Grunert. Greifswald, Leipzig. 
1841 B.M.; Camb.U.; Dub.N.L.I.; Dub.R.C.S.; Edinb.U.- 

Glasg.U.; Math.S.i.; Oxon.B.(R.); R.S.; U.C.L.i. 
See Arch. Mth. PS. 

xxiv 



List of Serial Publications 



G. Teix. J. Sc. 

Ha art. Ms. Teyl. Arcb. 
Haarl. Ntk. Vb. Mtsch. 

Haidinger Ab 

Haidinger B 



Ilain. Mm. S 

Hain. S. Mm. . . 



Hall Bij. 



Halle Ab. Nt. Vr. 



Halle Nf. Gs. B. 



Halle Z 

Halle Z. Nw. 



Hamb. Mth. Gs. Mt. . . 

Hammer schmiclt Al. 

Oestr. Z 

Hann. Arcbt.-Vr. Z. . . 
Harm. Z. Arcbt.-Vr. .. 

Heidi. Nt. Md. Vh 

Heidi. Vh. Nt. Md 



Helsingf. Acta. 
Helsingf. Bd. . 



Helsingf. Ofv 



lermbstadt Ms. . . . 



Jornal de Sciencias Mathematicas e Astronomicas, publicado pelo 

Dr Francisco Gomes Teixeira. Coimbra. 
1878 Math.S.; B.S.i. 

Archives du Musee Teyler. Haarlem. 

1866 B.M.; Camb.P.S.; Camb.U.; Dub.B.I.A.i.; Edinb.K.S.; 

Glasg.P.S.; N.H.M.; Oxon.B.; E.A.S.; E.S. 
Natuurkundige Verhandelingen van de [Bataafsche] Hollandsche 

Maatschappij der Wetenschappen te Haarlem. Haarlem. 
1799 B.M.; Camb.U. i.; Dub.R.D.S.; N.H.M.; B.S. 
Naturwissenschaftliche Abhandlungen ; Haidinger. Wien. 
184751. Camb.U.; Chem.S.i.; Edinb.B.S.i.; Linn.S.; N.H.M.; 

B.A.S.i.; B.S. 
Berichte iiber die Mittheilungen von Freunden der Naturwissen- 

schaften in Wien; Haidinger. Wien. 
184751. Camb.U.; Chem.S.i.; Edinb.B.S.; Linn.S.; N.H.M.; 

E.A.S.; B.S. 

) Memoires et Publications de la Societe des Sciences, des Arts et des 
( Lettres du Hainaut. Mons. 

1839 B.M.; Dub.T.C.i.; N.H.M.; Oxon.B.i.; E.S.i. 
Bijdragen tot de Natuurkundige Wetenschappen ; Hall, etc. 

Amsterdam. 

182632. B.M.; Camb.U.; N.H.M.; B.S. 
Abhandlungen des Naturwissenschaftlichen Vereins fur Sachsen und 

Thiiringen in Halle ; Giebel. Berlin. 
I860 B.M.; Camb.U.; N.H.M.i.; B.S.i. 
Bericht der Naturforschenden Gesellschaft zu Halle. Halle. 

1856 Camb.U.i.; Dub.B.D.S.i.; Dub.B.I.A.i.; Oxon.B.i.; B.S. 
\ Zeitschrift fur die gesammten Naturwissenschaften ; herausgegeben 
( von dem Naturwissenschaftlichen Vereine fur Sachsen und 

Thiiringen in Halle; Giebel. Berlin. 
1853 B.M.; Camb.U.i.; Dub.E.D.S.i.; Dub.R.I.A.i.; Dub.T.C.i.; 

Edinb.B.S.; Linn.S.; N.H.M.; Oxon.B.; Oxon.B.; B.S. 
See Z. Ww. 

Mitteilungen der Mathematischen Gesellschaft in Hamburg. Leipzig. 
1889 Math.S. 
Allgemeine Oesterreichische Zeitschrift fur den Landwirth, Forst- 

mann und Gartner; Hammerschmidt. Wien. 

jZeitschr. des Architekten- und Ingenieur- Vereins zu Hannover. 
| Hannover. 
1855 Camb.U.i.; P.O. 

\Verhandlungen des Naturhistorisch-Medicinischen Vereins zu Heidel- 
( berg. Heidelberg. 

1857 Camb.U.i.; Chem.S.i.; Dub.B.I.A.; Linn.S. i.; N.H.M.i.; 
B.S.i. 

Acta Societatis Scientiarum Fennicse. Helsingfors. 

1842 B.M.; Camb.P.S.; Camb.U.i.; Dub.B.I.A.; Edinb.B.S.i.; 

N.H.M.; Oxon.B.; B.A.S.; B.S. 
Bidrag till Kannedomen af Finlands Natur och Folk, utgifna af 

Finska Vetenskaps-Societeten. Helsingfors. 

1858 B.M.; Camb.P.S.i.; Camb.U.; Dub.E.I.A.; Edinb.B.S.i.; 
N.H.M.; Oxon.B.; B.A.S.; B.S. 

6'fversigt af Finska Vetenskaps-Societetens Forhandlingar. Hel- 
singfors. 

1853 B.M.; Camb.P.S.i.; Camb.U.i.; Dub.B.D.S.; Dub.B.I.A.; 
Edinb.E.S.i.; Glasg.U.i.; N.H.M.; Oxon.B.; E.A.S.; E.S. 

Museum des Neuesten und Wissenswiirdigsten aus dem Gebiete der 
Naturwissenschaft, der Kiinste, der Fabriken, der Manufakturen, 
der technischen Gewerbe, der Landwirthschaft, der Produkten- 
waaren und Handelskunde, und der biirgerlichen Haushaltung, 
etc.; Hermbstadt. Berlin. 

181418. B.M.; B.S. 

Hertha, Zeitschrift fur Erd-, Volker-, und Staaten-Kunde ; Berghaus 
und Hoffmann. Stuttgart und Tubingen. 

182529. B.M.; Camb.U.; Oxon.B.; E.S.; U.C.L.i. 

Journal of the Institute of Actuaries. London. 

1869 B.M.; Camb.U.; Dub.N.L.I.i.; Oxon.B.; E.A.S.i. 



I. CE. F. 



I. gypt. Bll. ............... 



I. Elect. E. J 

n Cim 

II Giamb. Vico 



n Pout. 



I. Bin. OTtl. T. 

IlProgresso 
Ing 



Inghirami Opnsc 

Innsb. Nt. Md. B 

Intell. Obs. 

Iowa Ac. Be. F 

Ir . Ac. Cunningham Mm. 



Ir. Ac. F. .. 



Ir. Ac.T 



List of Serial Publications 

Minutes of Proceedings of the Institution of Civil Engineers, con- 
taining Abstracts of the Papers and of the Discussions. London. 
1837 B.M.; Camb.P.S.; Camb.U.; Dub.R.C.S.; Dub.R.D.S.; 

Dub.B.I.A.; Edinb.K.S.; Edinb.U.; Glasg.P.S.i. ; Glasg.U.; 

Oxon.B.; Oxon.R.i.; P.O.; B.S.; U.C.L. 
See CE. X. F. 

Bulletin de 1'Institut Egyptien. Caire. 
1859 Camb.P.S.i.; Camb.U.i.; N.H.M.; U.C.L.i. 
Memoires ou Travaux Originaux pr^sentes et lus a 1'Institut Egyptien 

publics sous les auspices de S. A. Mohammed Said, vice-roi 

d'Egypte, sous la direction de M. le Docteur B. Schnepp. Paris 

& Caire. 

1862 Camb.P.S.i.; Camb.U.; N.H.M. 
Journal of the Institution of Electrical Engineers. London. 
1889 B.M.; Camb.U.; Dub.R.D.S.; Edinb.R.S.i.; Edinb.U.; 

Glasg.U.i.; Oxon.R.i.; P.O.; R.S.; U.C.L. 
II Cimento, rivista di Scienze, Lettere, ed Arti. Torino. 
185255. B.M. 

II Giambattista-Vico, giornale scientifico. Napoli. 
1857. N.H.M.; Oxon.B.i. 
See Giamb. Vico. 
II Politecnico; repertorio mensile di studj applicati alia prosperita 

e coltura sociale. 

II Politecnico ; repertorio di studj letterar j , scientific! e tecnici . Milano . 
183944; 1860 B.M.; P.O. 
Institution of Mechanical Engineers. Proceedings. Birmingham, 

London. 
1847 B.M.; Camb.P.S.i.; Camb.U.; Dub.R.D.S.; Glasg.U.; 

P.O.; R.S.; U.C.L. 
Transactions of the Institution of Mining and Metallurgy, London. 

London. 

1892 B.M.; Camb.U.i.; Geol.S.; N.H.M. ; P.O. 
II Progresso delle Scienze, Lettere, ed Arti. Napoli. 
First series undated ; Second series 1832 Camb.U.; Oxon.B. 
Der Ingenieur ; Zeitschrift fur das gesammte Ingenieurwesen ; 

Bornemann. Freiberg. 
184850. B.M.; P.O. 
Nuova Collezione di Opuscoli e Notizie di Scienze; Inghirami. 

Fiesole. 

182023. B.M. 

Berichte des Naturwissenschaftlich-Medizinischen Vereins in Inns- 
bruck. Innsbruck. 
1870 B.M.; Camb.U.; Dub.R.iXS.i.; Dub.R.I.A.i. ; Linn.S.i.; 

N.H.M.; Oxon.R.; R.S. 
The Intellectual Observer; a Review of Natural History, Microscopic 

Research, and Recreative Science. London. 
186268. B.M.; Camb.U.; Linn.S.; N.H.M.; Oxon.B.i.; Oxon.R.; 

P.O.; R.A.S.; R.S.i. 

Proceedings of the Iowa Academy of Sciences. Des Moines. 
1875 B.M.i.; Edinb.R.S.i.; N.H.M.; Oxon.B.i.; P.O.; R.S.i.; 

U.C.L.i. 

Royal Irish Academy. " Cunningham Memoirs." Dublin. 
1880 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.N.L.L; 

Dub.R.C.S.; Dub.R.D.S.; Dub.R.I.A. ; Dub.T.C.; Edinb.R.S.i.; 

Edinb.U.; Glasg.P.S.; Linn.S.; N.H.M.i.; Oxon.B.; Oxon.R.; 

R.A.S.; R.S.i.; U.C.L. 

Proceedings of the Royal Irish Academy. (Science.) Dublin. 
1841 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.N.L.L; 

Dub.R.C.S.; Dub.R.I.A.; Dub.T.C.; Edinb.R.S. ; Edinb.U.; 

Glasg.P.S.i.; Glasg.U.; Linn.S.; Math.S.i.; N.H.M.; Oxon.B.i.; 

Oxon.R.; P.O.i. ; R.A.S.; R.S. ; U.C.L.i. 
Transactions of the Royal Irish Academy. Science. Dublin. 
1787 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.N.L.L; 

Dub.R.D.S.; Dub.R.I.A.; Edinb.R.S.; Edinb.U.; Glasg.P.S.; 

Glasg.U.i.; Linn.S.; Math.S.i.; N.H.M.; Oxon.B.i.; Oxon.R.; 

P.O.i.; R.A.S.; R.S. ; U.C.L. 

India Review and Journal of Foreign Science and the Arts. Calcutta. 
183738. B.M.; N.H.M.i. 



List of Serial Publications 



Isere S. Bll. .. 
I. & S. I. J. 

Jap. As. S. T. 
Jb. Berg- Hw. 

J. Bt 

J.dePs 

J. dePs 

Jena. Sb 

Jena. Z 

J. Gen. Civ. .., 
J. H. Un. Cir. 

J. Mcr. Sc. . 



J. Mines 



J. Ps. C. . 



J. Sav 

J. Tel 

Kan. Ac. Sc. T. . 



Kan. TTn. Q 

Karlsruhe Nt. Vr. Vh. 
Karsten Arch. . . . 



Bulletin de la Society de Statistique, des Sciences Naturelles, et des 
Arts Industriels du departement de 1'Isere. Grenoble. 

1838 B.M.i.; N.H.M. ; Oxon.B. ; B.S.i. 

The Journal of the Iron and Steel Institute. London. 

1872 Camb.U. ; Chem.S.i. ; Dub.K.D.S. ; Dub.E.I.A. ; Dub.T.C.; 
Edinb.U.; Geol.M.i.; Glasg.P.S.i. ; Glasg.U.i.; Oxon.B.; P.O.; 
B.S.; U.C.L. 

Transactions of the Asiatic Society of Japan. Yokohama. 

1872 B.M. ; Camb.U. ; Edinb.B.S. ; N.H.M. ; Oxon.B. ; Oxon.E.; 
P.O.*.; B.S. 

Jahrbuch fur das Berg- und Hiittenwesen im Konigreiche Sachsen. 
Freiberg. 

1873 B.M.; N.H.M.i. ; P.O. 
The Journal of Botany. London. 

1863 B.M.; Camb.U.; Dub.N.L.I.i. ; Dub.K.C.S.; Glasg.U. ; 
Linn.S. ; N.H.M.; P.O.i. 

Journal de Physique, de Chimie, et de 1'Histoire Naturelle; 

de Lametherie etc. Paris. 
1794-1823. B.M. ; Camb.U.; Glasg.U. i. ; N.H.M.i.; Oxon.B.; 

Oxon.B.; E.S.; U.C.L.i. 

Journal de Physique Theorique et Appliquee; D' Almeida. Paris. 
1872 Camb.U.; Dub.B.C.S.; Glasg.U.i.; Oxon.B.; P.O.; E.S. 
Sitzungsberichte der Jenaischen Gesellschaft fur Medicin und 

Naturwissenschaft. Jena. 

187786. Edinb.B.S.i. ; Linn.S.i.; Oxon.E.; E.S. 
Jenaische Zeitschrift fur Naturwissenschaft, herausg. von der 

Medicinisch-Naturwissenschaftlichen Gesellschaft zu Jena. Jena. 

1864- B.M.; Camb.P.S. i.; Camb.U.; Chem.S.i.; Dub.N.L.I.i.; 
Dub.B.D.S.i.; Edinb.E.S. ; Edinb.U.i. ; Glasg.U.i.; Linn.S.; 
N.H.M.; Oxon.B.; Oxon.E.; E.S.; U.C.L. 

Journal du Genie Civil des Sciences et des Arts. Paris. 

182848. B.M.i.; Camb.U.; P.O. 

The Johns Hopkins University Circulars. Baltimore. 

1879 Camb.P.S. ; Camb.U. ; Dub.N.L.I.i. ; Dub.B.I.A.i. ; 

Edinb.E.S. i. ; Edinb.U. ; Glasg.P.S. ; Math.S.i. ; N.H.M. ; 

Oxon.B.; Oxon.E.; E.A.S.i.; E.S.; U.C.L.i. 
Quarterly Journal of Microscopical Science; Lankester and Busk. 

London. 
1853 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.N.L.I. ; 

Dub.E.C.S. ; Edinb.E.S. ; Edinb.U. ; Glasg.P.S. ; Linn.S. ; 

N.H.M.; Oxon.B.i. ; Oxon.E.; P.O.; E.S.; U.C.L. 
Journal des Mines, ou Eecueil de Memoires sur 1' exploitation des 

Mines, et sur les Sciences et les Arts qui s'y rapportent. Paris. 
17941815. B.M.; Camb.U.; Dub.T.C.; Edinb.E.S.; Linn.S.i.; 

N.H.M.; Oxon.B. (E.) ; E.S.i. 
The Journal of Physical Chemistry. Ithaca, N.Y. 
1896 B.M. ; Camb.P.S. ; Camb.U. ; Chem.S. ; Edinb.E.S. ; 

Edinb.U.; Glasg.U.; Oxon.E.; P.O.; E.S.i. 
Journal des Savants. Paris. 
1816 B.M.; Camb.U.; Dub.N.L.I.; Dub.T.C.; Edinb.E.S.i.; 

Glasg.U.i.; Oxon.B.; Oxon.B.; P.O.i.; E.S. 
Journal Telegraphique publie par le Bureau International des 

Administrations Telegraphiques. Berne. 
1869 P.O. 

Transactions of the Kansas Academy of Science. Topeka, Kansas. 
1872 Camb.P.S.i. ; Dub.E.I.A.; Edinb.E.S.i.; Glasg.P.S.i.; 

Linn.S.i; N.H.M.; Oxon.B.i.; B.S.i. 
The Kansas University Quarterly. Laurence, Kansas. 
1893 B.M.i. ; Dub.E.D.S.i. ; Dub.E.I.A.i. ; Edinb.E.S.i. ; Glasg. 

P.S.i.; Math.S.; N.H.M.; E.S. 
Verhandlungen des Naturwissenschaftlichen Vereins in Karlsruhe. 

Karlsruhe. 

1864 B.M.i.; Dub.E.I.A.; N.H.M. 
Archiv fiir Mineralogie, Geognosie, Bergbau, und Hvittenkunde ; 

Karsten. Berlin. 
182955. B.M.; Edinb.E.S.i.; Geol.M.; N.H.M.; P.O.; E.S. 



List of Serial Publications 



Kastner Arch. Ntl. 

Kazan Mm . TTn 

Kazan 8. Nt. (Ps.-Mth.) T, 

Kazan S. Ps.-Mth. Bll. .. 
Kazan TTn. Bll 

Kazan Un. Mm 

Kharkov Mth. 8. Com.... 



Kiel Schr. 



Kiob. Dn. Vd. Sclsk. Af h. 
Kjob. Dn. Vd. Selsk. Af h. 



Kiob. Dn. Vd. Selsk. Skr. 
Kjbb. Dn. Vd. Selsk. Skr. 



Kjob. Dn. Vd. Selsk. Skr. 
Kibb.Skr 



Kiob. Ov 

Kjob.0v! '.'.".'.'.'.'. 
Konigsb. Arch. 

Konigsb. Schr... 



Krk. Ak. (Mt.-Prz.) Pam. 



Krk. Ak. (Mt.-Prz.) Rz.... 
Krk. Ak. (Mt.-Prz.) Hz. 

* Bp 

Krk. Roczn. Tow. Nauk. 
Krk. Roczn. Uniwers. 



Arcbiv f fir die gesammte Naturlehre ; Kastner. Niimberg. 

182435. B.M.; N.H.M.; P.O. 

Scientific Memoirs published by the Imperial University of Kazan. 

Kazan. 
1834 B.M.i.; Camb.U.; Dub.E.I.A. ; Edinb.E.S.i.; Glasg.P.S.i.; 

Linn.S.i.; B.S.i. 
See Kazan Un. Mm. 
Proceedings of the Physico-Mathematical Section of the Naturalists' 

Society of the Imperial University of Kazan. Kazan. 
188390. U.S. 

Bulletin de la Societe Physico-Mathematique de Kasan. Kasan. 
1891 Dub.B.I.A.i.; Edinb.B.S.i. ; B.S.i. 
Bulletin of the Imperial University of Kazan. Kazan. 
1865 B.M.i. ; Camb.U.i. ; Edinb.B.S.i.; Linn.S.i. 
See Kazan Mm. Un. 
Communications and Proceedings of the Mathematical Society of 

the Imperial University of Kharkov. Kharkov. 
1879? E.S.i. 

Schriften der Universitat zu Kiel. Kiel. 
185580. B.M.; Camb.U.; Dub.R.I.A.; Edinb.B.S.i.; N.H.M.i.; 

Oxon.B.; E.S. 

I Det Kongelige Danske Videnskabernes Selskabs naturvidenskabelige 
\ og mathematiske Afhandlinger. Kiobenhavn. 
( 182446. B.M. ; Dub.T.C. ; Edinb.E.S. ; Linn.S.i. ; N.H.M. ; E.S. 
( Det Kongelige Danske Videnskabernes Selskab Skrivter. Kiobenhavn. 
{180118. B.M.; Camb.P.S. i.; Camb.U.; Edinb.E.S.; N.H.M. ; 
I Oxon.B.; B.S. 

See Dn. Vd. Selsk. Skr. 
/Det Kongelige Danske Videnskabernes Selskabs Skrifter. Natur- 

videnskabelig og Mathematisk Af deling. Kj^benhavn. 
1 1849 B.M. ; Camb.U. i. ; Edinb.E.S. ; Linn.S. ; N.H.M. ; E.A.S. ; 
| E.S.; U.C.L.t. 
/Oversigt over det Kongelige Danske Videnskabernes Selskabs For- 

handlinger. Kjdbenhavn. 

Jl806 Camb.P.S.; Camb.U.i.; Chem.S.i. ; Dub.E.D.S.i. ; Dub. 
E.I.A.i. ; Dub.T.C.i. ; Edinb.E.S.i. ; Glasg.U.i. ; Linn.S.i. ; 
( N.H.M.i.; Oxon.E.; P.O.i.; E.A.S.i.; E.S. 
Konigsberger Archiv fiir Naturwissenschaften und Mathematik ; 

Bessell, etc. Konigsberg. 
1812. B.M. ; Camb.U.; Linn.S. 
Schriften der koniglichen Physikalisch-Oekonomischen Gesellschaft 

zu Konigsberg. Konigsberg. 
I860 B.M.; Camb.P.S.; Dub.E.I.A. ; Edinb.E.S.i.; Linn.S.; 

N.H.M.; P.O.i.; E.S. 

Kosmos. Czasopismo polskiego Towarzystwa przyrodnik6w imienia 
Kopernika. [Cosmos. The Journal of the Polish Society of 
Naturalists founded in honour of Copernicus.] Lwow. 
1876 B.M.; N.H.M. 

Pamitnik Akademii Umiejtnosci w Krakowie. Wydzia-l- Mate- 
matyczno-Przyrodniczy. [Memoirs of the Academy of Science 
in Cracow. Section of Mathematics and Natural Science.] 
Krakow. 

1874 B.M.; Edinb.E.S.i.; N.H.M. 

Eozprawy Wydziatu Matematyczno - Przyrodniczego Akademii 
Umieje,tnosci. [Proceedings of the Section of Mathematics and 
Natural Science of the Academy of Science.] Krak6w. 
1874 B.M.; Edinb.E.S.i.; N.H.M. 

Eocznik Towarzystwa Naukowego z Uniwersytetem Krakowskim 
Polaczonego. Krakowie. [Annals of the Scientific Society of the 
Polish University of Krakow. Krakow.] 
181772. B.M. 



Lane. Hist. 8. T i Proceedings and Papers of the Lancashire and Cheshire Historic 

Lane. T. Hist. 8 { Society. Liverpool . 

184954. Continued as: Transactions, etc., 1855 B.M. ; 

Camb.U.i.; Dub.E.I.A.i.; Edinb.E.S.i.; Glasg.P.S.i.; Oxon.B. i.; 

E.S. 



List of Serial Publications 



Laus. Bll. S. Vd. 
Laus. 8. Vd. Bll. . 



Leic. S. T. 



Leijd. A. Ac 

Leip. Ab. Jablon. Gs 



Leip. Ab. rath. Ps. 



Leip. As. 6s. Vjschr. 
Leip. B 



Leip. Jablon. Preisschr. 



Leip. Mth. Ps. Ab 

Leip. Mtlx. Ps. B 

Le mans S. R. Tr. . . . 



Les Mondes 



Liege A. Ac.. 



Liege Mm. S. Sc. 
Liege S. Sc. Mm. 



Lille Mm 

Lille Mm. S 

LilleS. Mm 

Lille Tr. .. 



Lille Tr. Mm 

Lindenau Z 



( Bulletin des Seances de la Societe Vaudoise des Sciences Naturelles. 
| Lausanne. 

1842 Dub.E.D.S.i. ; Dub.E.I.A.i. ; Edinb.E.S.i. ; Linn.S.; 
N.H.M.; Oxon.B. i.; E.S. 

The Transactions of the Leicester Literary and Philosophical Society. 



1835 Camb.U.; Dub.K.D.S.; Geol.S.; Glasg.P.S.; Linn.S.i.; 

N.H.M.i. ; Oxon.B.; P.O.; U.C.L. 
Annales Academies Lugduno-Batavse. Leijden. 
181575. B.M.; Camb.U.; Dub.T.C.i.; N.H.M.; Oxon.B.; B.S.i.; 

U.C.L.i. 
Abhandlungen bei Begriindung der k. Sachsischen Gesellschaft der 

Wissenschaften am Tage der zweihundertjahrigen Geburtsfeier 

Leibnizens; herausg. v. d. Jablonowski'schen Gesellschaft zu 

Leipzig. Leipzig. 

1846. Camb.U.; Dub.E.I.A.; Edinb.E.S.; N.H.M.; E.A.S.; E.S. 
Abhandlungen der Mathematisch-Physischen Classe der Koniglich 

Sachsischen Gesellschaft der Wissenschaften. Leipzig. 
1852 B.M.; Camb.P.S.; Camb.U.; Dub.E.I.A.; Edinb.E.S.; 

Glasg.U. ; Math.S.i. ; N.H.M.; Oxon.B.; P.O.; E.A.S.; E.S. ; 

U.C.L. i. 

See Leip. Mth. Fs. Ab. 

Vierteljahrsschrift der Astronomischen Gesellschaft. Leipzig. 
1866 B.M.; Camb.P.S.i.; Camb.U.; Dub.E.I.A.; Edinb.E.S.; 

Oxon.B.; E.A.S.; E.S. 

Berichte liber die Verhandlungen (Math.-Phys. Classe) der Konig- 
lich Sachsischen Gesellschaft der Wissenschaften zu Leipzig. 

Leipzig. 

1846 B.M.; Camb.P.S.; Camb.U.; Dub.E.I.A.; Edinb.E.S.; 
Glasg.U.; Math.S.i.; N.H.M.; Oxon.B.; Oxon.E.; E.A.S.; E.S.; 
U.C.L.i. 

See Leip. Mth. Ps. B. 

Preisschriften gekront und herausgegeben von der Fiirstlich Jab- 
lonowski'schen Gesellschaft zu Leipzig. Leipzig. 

1847 B.M. ; Camb.U. ; Dub.E.I.A. ; Edinb.E.S.i. ; N.H.M. ; 
Oxon.B.; E.A.S.i.; B.S.i.; U.C.L.i. 

See Leip. Ab. Mth. Fs. 

See Leip. B. 

Analyse des Travaux de la Societe [Eoyale] des Arts du Mans. 

Le Mans. 

1820. N.H.M.; E.S. 

Les Mondes, Eevue hebdomadaire des Sciences et de leurs Appli- 
cations aux Arts, et a 1'Industrie; l'Abb6 F. Moigno. Paris. 
1863 B.M.; Camb.U.i.; Dub.N.L.I.i.; Glasg.P.S.i.; Oxon.E.; 

P.O.; B.S.i. 
L'Institut; Journal des Academies et Societes Scientifiques de la 

France et de 1'Etranger. Paris. 
1833 B.M.i.; Camb.U.; Dub.T.C.; Edinb.E.S.i.; Glasg.P.S.i.; 

N.H.M.; Oxon.B. (E.); P.O.i.; E.S.i. 
Annales Academise Leodiensis. Liege. 

181727. B.M.; Camb.U.; Dub.T.C.; N.H.M.; Oxon.B.; E.S. 
Memoires de la Societe [Eoyale] des Sciences, de 1' Agriculture, et 

des Arts a Liege. Liege. 
1843 B.M.; Camb.U.; Dub.T.C.; Edinb.E.S.i.; Glasg.P.S.i. ; 

Glasg.U.i.; Linn.S.i.; N.H.M.; Oxon.B.; P.O.; E.S. 
Memoires de la Societe [Eoyale] des Sciences, etc. a Lille. Lille. 
1827 B.M.; Camb.U.; Dub.T.C.; N.H.M. ; Oxon.B.; Oxon.E.; 

E.S.i. 
Eecueil des Travaux de la Socie'te' d' Amateurs des Sciences, de 

1' Agriculture, et des Arts a Lille. Lille. 
181927. B.M.; Camb.U.; Dub.T.C.; N.H.M.; Oxon.B.; Oxon.E.; 

E.S. 

Travaux et Memoires de 1'Universite de Lille. Lille. 
1889 Camb.P.S.; Camb.U.; Dub.E.D.S.; Dub.E.I.A.; N.H.M.; 

E.S. 
Zeitschrift f iir Astronomic und verwandte Wissenschaften ; Lindenau. 

Tubingen. 
181618. B.M.; Camb.U.; E.A.S.; E.S. 

xxix c 2 



Liouv. J. 

Liouv. J. Mth. . 



Lisb. A. 



Lisb. J. Sc. Mth. 



Lisb. Mm. 
Lisb. Mm. Ac. Sc. [ 
Lisb. Mm. Sc. ] 

L. Mth. S. F. . 



. V.-St 

Lotos 

Xiouvain A. Ac 

Lpldina 

Lpool Lt. Ph. S. P 

L. Ps. S. P 

Lucca At. Ac 

Lum. Elect. 

Lund. Acta XTn 

Lund Phys. Sallsk. Ts. 

Lund . Tin. Acta 

Lux. I. R. Pb. ... 



Lux. S. Sc. Mm 

Lux. S. Sc. Nt. 

Lyon Ac. Mm. (Be.) . . . . 

Lyon Ac. Sc. Mm 



List of Serial Publications 

Journal de Mathe'matiques pures et appliquees, fonde par Joseph 

Liouville. Paris. 
1836 B.M. ; Camb.U. ; Dub.E.I.A. ; Edinb.R.S.i. ; Edinb.U.; 

Glasg.P.S.i.; Glasg.U.; Math.S.i.; Oxon.B.(B.); E.S.; U.C.L. 
Annaes das Sciencias e Lettras, publicados debaixo dos auspicios da 

Academia Eeal das Sciencias: Sciencias mathematicas, physicas, 

historico-naturaes, e medicas. Lisboa. 

1857 B.M.; Dub.E.I.A.; Edinb.E.S.i.; N.H.M.; E.A.S.i.; B.S.i. 
See A. Sc. 
Historia e Memorias da Academia Real das Sciencias de Lisboa. 

Lisboa. 
1797 B.M.; Camb.U.; Edinb.B.S.; N.H.M.; Oxon.B.; E.A.S.; 

E.S.i. 

See Lisb. Mm., Lisb. Mm. Ac. Sc. and Lisb. Mm. Sc. 
Jornal de Sciencias mathematicas, physicas e naturaes. Publicado 

sob os auspicios da Academia E. das Sciencias de Lisboa. Lisboa. 
1868 B.M.; Camb.U.; Dub.E.D.S.i. ; Edinb.E.S.i.; Linn.S. ; 

Math.S.i.; N.H.M.; Oxon.B.; E.A.S.; E.S.; U.C.L.i. 

See Lisb. Ac. Sc. Mm. 

Proceedings of the London Mathematical Society. London. 
1865 B.M. ; Camb.P.S. ; Camb.U.; Dub.E.I.A.; Dub.T.C. ; 

Edinb.E.S.; Edinb.U.; Glasg.U.; Math.S.; Oxon.B.i.; Oxon.B.; 

E.S.; U.C.L. 
Die landwirthschaftlichen Versuchs-Stationen. Organ fur wissen- 

schaftliche Forschungen auf dem Gebiete der Landwirthsehaft. 

Dresden, Chemnitz. 

1859 B.M.i.; Camb.U.; Chem.S.i.; Oxon.B.; P.O.i.; E.S.i. 
Lotos. Zeitschrift fur Naturwissenschaften. Prag. 
185195. B.M.; Camb.U.; Dub.E.I.A.i.; N.H.M. 
Annales Academise Lovaniensis. Bruxelles, Louvain. 
182127. B.M.; Camb.U.; Dub.T.C.; Oxon.B.; E.S. 
Leopoldina : amtliches Organ der Kaiseiiichen Leopoldino-Caro- 

linischen Deutschen Akademie der Naturforscher. Dresden. 
1859 B.M.; Camb.P.S.; Camb.U.i.; Edinb.E.S.i.; Linn.S.; 

N.H.M.; E.A.S.i.; E.S. 
Proceedings of the Literary and Philosophical Society of Liverpool. 

London, Liverpool. 
1844 B.M.; Camb.U.i.; Chem.S.i.; Dub.E.I.A.; Edinb.E.S.i.; 

Glasg.P.S.; Linn.S.; N.H.M.; Oxon.B.i.; P.O.i.; E.A.S.i.; E.S.; 

U.C.L.i. 

Proceedings of the Physical Society of London. London. 
1874 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.E.C.S.; Dub. 

E.D.S.; Dub.E.I.A.; Dub.T.C.; Edinb.E.S.i.; Glasg.P.S.i.; 

Glasg.U.i.; Math.S.; Oxon.B.; Oxon.E.; P.O.; E.A.S.; E.S.; 

U.C.L.i. 

Atti della E. Accademia Lucchese di Scienze, Lettere, ed Arti. Lucca. 
1821 B.M.; Camb.U.; Dub.T.C.i.; Oxon.B.i. 
La Lumiere Electrique. Journal universel d'Electricite". Paris. 
187994. B.M.; Glasg.U.i.; P.O. 
Acta Universitatis Lundensis. Lunds Universitets Ars-skrift. Afdel- 

ningen for Mathematik och Naturvetenskap. Lund. 
1864 B.M.; Camb.P.S.; Camb.U.; Dub.E.I.A.; Edinb.E.S.i.; 

Linn.S.i.; N.H.M.; Oxon.B.; E.S. 
See Lund. Tin. Acta. 

Physiografiska Sallskapets Tidskrift. Lund. 
183738. Camb.U.; N.H.M.; E.S. 
See Lund. Acta TTn. 
Publications de 1'Institut Eoyal Grand-Ducal de Luxembourg. 

Section des Sciences Naturelles et Math&natiques : ci-devant 

"Societe des Sciences Naturelles." Luxembourg. 
1870 Dub.B.D.S.; Dub.E.I.A.; Edinb.E.S.i.; N.H.M.; E.S.i. 
[Societe des Sciences Naturelles du Grand-Duche de Luxembourg. 
j Luxembourg. 
1185369. Dub.E.I.A.; E.S. 

(Memoires de 1' Academic des Sciences, Belles-Lettres et Arts de 
( Lyon. Classe des Sciences. Lyon, Paris. 



List of Serial Publications 



Lyon A. a. Ag. 



Lyon Mm. Ac 

Lyon Mm. Ac. Sc. 
Lyon S. A. Ag. . . . 
Lyon 3. Ag. A. ... 
Lyon TTn. A 



Maclurian Lyceum Ct. 

Macon Ac. A 

Macon S. C. R 

Madras E ng. Rp 



Madras J. 



Madrid Ac. Ci. Mm 

Madrid Mm 

Madrid Rv. .. 



Mag. Ale. Ets 

Mag. Ak. Ets. (Mth. Term.) 



Magdeb. Wt. Vr. Jbr. u. 
Ab 

Mag. Tud. Alt. Etlt. (Mth.) 



Mag. Tud. Ak. Ets 

Majocchi A. Fis. C 

Manch. Lt. Ph. S. Mm.... 



Mancb. Lt. Ph. S. Mm. 
& P. .. 



1845 B.M.; Camb.U.; Edinb.B.S.i.; Linn.S.i.; N.H.M.; Oxon.B.; 

B.S.i. 

See Lyon Mm. Ac. and Lyon Mm. Ac. Sc. 
Annales des Sciences physiques et naturelles, d' Agriculture, et 

d'Industrie, publiees par la Societe d' Agriculture, etc. 
Annales de la Societe d' Agriculture, Histoire Naturelle et Arts 

Utiles de Lyon. Lyon. 
1838 B.M.; Camb.U.; Dub.B.I.A.; Linn.S.; N.H.M.; Oxon.B.; 

P.O.; B.S. 
See Lyon S. A. Ag. and Lyon 8. Ag. A. 

See Lyon Ac. Mm. (Sc.) and Lyon Ac. Sc. Mm. 

See Lyon A. S. Ag. 

Annales de 1'Universite de Lyon. Paris, Lyon. 
1891 B.M.; Edinb.B.S.; N.H.M.i.; B.S.i. 

Contributions of the Maclurian Lyceum to the Arts and Sciences. 

Philadelphia. 

182729. B.M.; Linn.S.i.; N.H.M. 
Annales de 1'Acade'mie de Macon, Societe des Arts, Sciences, Belles- 

Lettres et d' Agriculture. Macon. 
1851 B.M. E.S.i. 
Compte Bendu des Travaux de la Societe (d' Agriculture,) des 

Sciences, Arts et Belles-Lettres, de Macon. Macon. 
180752. B.M.i.; E.S.i. 
Beports, etc. on various professional subjects connected with the 

duties of the Corps of Engineers of the Madras Presidency; 

Capt. J. T. Smith, F.B.S. Madras. 
183946. P.O.; B.S. 

The Madras Journal of Literature and Science. Madras. 
1833 B.M.i.; Camb.U.; Dub.N.L.I.i.; Linn.S.i.; N.H.M.; Oxon. 

B.i.; P.O.; B.A.S.i.; B.S.i.; U.C.L.i. 

IMemorias de la Beal Academia de Ciencias. Madrid. 
1850 B.M.; Camb.U.i. ; Dub.B.I.A.; Dub.T.C.; Edinb.E.S.; 
Linn.S.i.; N.H.M.; Oxon.B.; B.A.S.i.; B.S.i.; U.C.L.i. 
Bevista de los Progresos de las Ciencias exactas, fisicas, y naturales. 

Madrid. 
185086. B.M.; Dub.E.D.S.i.; Edinb.B.S.i.; N.H.M.; Oxon.B.i.; 

E.A.S.i.; B.S.i. 

Magyar akademiai Ertesito. [Beport of the Hungarian Academy.] Pest. 
184059. B.M. 
Magyar akademiai Ertesito. A mathematikai es term6szettudo- 

manyi osztalyok kozlonye. [Beport of the Hungarian Academy. 

Communications of the Mathematical and Natural Science 

sections.] Pest. 

186065. B.M.; Camb.P.S.i.; B.S. 
Jahresbericht und Abhandlungen des Naturwissenschaftlichen 

Vereins zu Magdeburg. Magdeburg. 
1869 B.M.; B.S.i. 
Ertekez6sek a Mathematikai Osztaly korebol. Kiadja a Magyar 

Tudomanyos Akademia. [Memoirs on Mathematical subjects. 

Published by the Hungarian Academy of Science.] Pest. 
1867-94. B.M.; Edinb.B.S.i.; B.S. 
A Magyar Tudomanyos Akademia Ertesitoje. [Beport of the 

Hungarian Academy of Science.] Pest. 
1867 B.M. 
Annali di Fisica, Chimica, e Matematiche, col Bulletino dell' 

Industria meccanica e ehimica ; Majocchi. Milano. 
184150. B.M.; B.S. 
Memoirs of the Literary and Philosophical Society of Manchester. 

London and Manchester. 
17851887. B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.B.D.S.; 

Dub.B.I.A.; Glasg.P.S.i.; Linn.S.; Math.S.i.; N.H.M.; Oxon.B.; 

Oxon.B.; P.O.; B.A.S.i.; B.S.; U.C.L.i. 

See Mancb. Mm. Ph. a., Manch. Ph. S. Mm. and Manch. S. Mm. 
Memoirs and Proceedings of the Manchester Literary and Philo- 
sophical Society. Manchester. 

xxxi 



Manch. Lt. Ph. 8. P. 



Blanch. Mm. Ph. s. 
Blanch. Ph. 8. Mm. 
Blanch. Ph. 8. P. ..'. 

Blanch. 8. Mm 

Blanch. 8. P 

Mart. Schr 



Mars. Fac. Sc. A. 

Mathematician .. 

Mathesis 

Mbl . Nt. . 



Medley I. Eng 

Mengelwerk Wisk. 



M.-et-L. Mm. 8. Ac. 
Met. 8. QJ 



Metz Ac. Mm 

Metz Mm. Ac 

Mex. Arch. Com. Sc 



Blex. Beg. Trim., 

Mex. 8. "Alzate" Mm. 
Big. Ntvd. 



Midi. Ntlist. 

BUI. At. X. Lomb. 



List of Serial Publications 

1888 BM; Camb.P.S. ; Camb.U. ; Chem.S. ; Dub.E.I.A.i.; 

Edinb.E.S.; Glasg.P.S.; Linn.S.; Math.S.; N.H.M.; Oxon.B.; 

OxonE.; P.O.; E.A.S.; E.S.; U.C.L.i. 
Proceedings of the Literary and Philosophical Society of Manchester. 

Manchester. 
185787. B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.E.D.S.; 

DubE.I.A.; Dub.T.C.; Edinb.E.S.; Glasg.P.S.; Linn.S.; Math. 

S.i.; N.H.M.; Oxon.B.; P.O.; E.A.S.; E.S.; U.C.L.i. 
See Blanch. Ph. 8. P. 
I See Blanch. Lt. Ph. 8. BIm. 

See Blanch. Lt. Ph. 8. P. 
See Blanch. Lt. Ph. 8. Mm. 
See Blanch. Lt. Ph. 8. P. 

Schriften der Gesellschaft zur Beforderung der gesammten Natur- 

wissenschaften zu Marburg. Marburg. 
1823 B.M.i.; Camb.U.; N.H.M.; Oxon.E.; E.S. 
Annales de la Faculte des Sciences de Marseille. Marseille, 

Paris. 
1891 B.M.; Camb.P.S.; Dub.E.I.A.; Edinb.E.S.; Glasg.P.S.; 

Linn.S.; Math.S.i.; N.H.M.; E.A.S.; E.S. 
The Mathematician ; Davies, etc. London. 
184550. B.M.; Camb.U.; Dub.T.C.; Oxon.B.; E.S. 
Mathesis. Eecueil Mathematique.... Gand, Paris. 
1881 B.M.; Camb.U. 

Maanblad voor Natuurwetenschappen, uitgegeven door de Sectie voor 
Natuurwetenschappen van het Genootschap ter Bevordering van 
Natuur-, Genees- en Heelkunde. Amsterdam. 
1871 N.H.M. 
Professional Papers on Indian Engineering; Major J. G. Medley. 

Eoorkee. 

186468. P.O.i.; E.S. 

Mengelwerk van uitgeleezene en andere Wis- en Natuurkundige Ver- 
handelingen ; door het Genootschap der Mathematische Weten- 
schappen, etc. Amsterdam. 
17961816. E.S. 
See Amst. Mengelwerk. 

The Messenger of Mathematics. Cambridge, London. 
1862 B.M.; Camb.P.S.; Camb.U.; Dub.N.L.I.i.; Dub.E.C.S.i.; 
Dub.E.D.S. i.; Edinb.E.S.i. ; Edinb.U.; Glasg.U. ; Math.S.i.; 
Oxon.B.; Oxon.E.; E.S.; U.C.L. 

Memoires de la Societe Academique de Maine et Loire. Angers. 
1857 B.M.; Camb.U.; N.H.M.; E.S.i. 

. Quarterly Journal of the Eoyal Meteorological Society. London. 
1873 Camb.U.; Dub.E.I.A.i.; Dub.T.C.i.; Edinb.E.S.; Linn. 

S.i.; Oxon.E.; P.O.; E.A.S.; E.S. 
. Meteorologische Zeitschrift. Berlin. 

1884 Camb.U.; Edinb.E.S.; P.O.; E.S. 
, \Memoires de I'Acad&nie (Eoyale, Imperiale) de Metz. Metz. 

J1821 B.M.; Camb.U.; Dub.T.C.; N.H.M.; Oxon.B.; E.S.i. 
. Archives de la Commission Scientifique du Mexique, publiees sous 

les auspices du Ministere de 1'Instruction Publique. Paris. 
186569. Oxon.B.; E.S. 
. Eegistro trimestre, 6 Coleccion de Memorias de Historia, Literatura, 

Ciencias, etc., por una Sociedad de Literates. Mexico. 
183233. 

Memorias de la Sociedad Cientifica "Antonio Alzate." Mexico. 
1887 B.M.i.; Camb.P.S.; Dub.E.I.A.; Edinb.E.S.; Linn.S.i.; 

Math.S.i.; N.H.M.i.; E.A.S.; E.S.; U.C.L.i. 
. Magazin for Naturvidenskaberne ; Lundh, etc. Christiania. 

182336. B.M.; N.H.M.i.; E.S. 
. Monatshefte fur Mathematik und Physik. Wien. 

1890- B.M.; Camb.U.; Edinb.U.; Math.S.i.; N.H.M. 
.. The Midland Naturalist. London, Birmingham. 

187893. Camb.U.; Geol.M.; Linn.S.; P.O. 
. Atti dell' I. E. Istituto Lombardo di Scienze, Lettere, ed Arti. 

Milano. 
185864. B.M.; Camb.U.; Edinb.E.S.; N.H.M.; Oxon.B.; E.S. 

xxxii 



List of Serial Publications 



Mil. Effem 

Mil. Effem. As. . 

Mil. Ephem. As.. 



Mil. G. I. Lomb. 



Mil. G. a. Inc. 



Mil. I. Lomb. G 

Mil. I. Lomb. Mm.. 



Mil. I. Lomb. Bd. 



MiL Mm. I. tomb 

Mil. Mm. I. Lomb. Ven. 



Mitan Arb. Kurland. Gs. 



Mi tan Quatember 



Mitan Send. Kurland. Gs. 



Mntp. Ac. Mm. 



Mntp. Ac. PV. . . . 



Mntp, Ac. Sc. Mm. 

Mntp. Mm. Ac j. 

Mntp. Mm. Ac. Sect. Sc. } 
Mntp. Mm. Ac. Sect. Md. 



Mntp. Rec. Bll. 



Mod. Ac. Sc. Mm. 
Mod. Mm. Ac. Sc. 



Mod. Mm. 8. It. 
Mod. S. It. Mm. 



(Effemeridi Astronomiche di Milano. Con Appendice di Osservazioni 
\ e Memorie Astronomiche. Milano. 
(1806 Camb.U.; Oxon.B.; B.A.S.t. 
Ephemerides Astronomicae, ad Meridianum Mediolanensem supputatffl 

ab Angelo de Cesaris. Accedit Appendix cum Observationibus et 

Opusculis. Mediolani. (Milan.) 
1774_1805. Oxon.B. 
Giornale dell' I. B. Istituto Lombardo di Scienze, Lettere, ed Arti, 

e Biblioteca Italiana ; compilata da varj dotti nazionali e stranieri. 

Milano. 

184156. B.M.; N.H.M.; Oxon.B.; B.S. 
See Mil. I. Lomb. G. 
Giornale della Societad' Incorragiamento delle Scienze, etc. stabilita 

in Milano. Milano. 
180865. B.M.; Camb.U. 
See Mil, a. I. Lomb. 

Memorie dell' I. B. Istituto Lombardo di Scienze, etc. Milano. 
1843 B.M.; Camb.P.S.; Camb.U.; Dub.B.I.A.; Dub.T.C.; 

Edinb.B.S.t.; Math.S.t.; N.H.M.; Oxon.B.; B.A.S.t.; B.S.; 

U.C.L.t. 

See Mil. Mm. I. Lomb. 

Beale Istituto Lombardo di Scienze e Lettere. Bendiconti. Milano. 
1864 B.M.; Camb.P.S.; Camb.U.; Dub.B.I.A.; Edinb.B.S.t.; 

Math.S.t.; N.H.M.; Oxon.B.t.; B.A.S.t.; B.S.; U.C.L.t. 
See Mil. I. Lomb. Mm. 

Memorie dell' I. B. Istituto del regno Lombardo- Veneto. Milano. 
181938. B.M.; Camb.U.; N.H.M.; Oxon.B. i.; B.S. 
Arbeiten der Kurlandischen Gesellschaft fur Literatur und Kunst. 

Mitau. 

184751. B.M.; Camb.U. 
Die Quatember; Zeitschrift fur naturwissenschaftl., geschichtl., 

philolog. und gemischte Gegenstande; von Trautvetter. Mitau. 
182930. B.M. 
Sendungen der Kurlandischen Gesellschaft fur Literatur und Kunst. 

Mitau. 

1840-47. B.M. 
The Mineralogical Magazine and Journal of the Mineralogical 

Society of Great Britain and Ireland. Truro, London. 
1876 B.M.; Camb.U.; Chem.S.t.; Dub.N.L.I.; Geol.M.; N.H.M.; 

Oxon.B.(B-); P.O.; B.S. 
Academic des Sciences et Lettres de Montpellier. Memoires de la 

Section des Sciences. Montpellier. 
1847- B.M.; Camb.U.; Dub.E.D.S.; Dub.B.I.A.; Edinb.E.S.; 

Linn.S.t.; N.H.M.; Oxon.B.; B.A.S.; E.S.; U.C.L.t. 
See Mntp. Ac. Sc. Mm., Mntp. Mm. Ac. and Mntp. Mm. Ac. 

Sect. Sc. 
Extraits des Proces-Verbaux des Seances de 1' Academic des Sciences 

et Lettres, etablie a Montpellier. Montpellier. 
184754. N.H.M.t. 

See Mntp. Ac. Mm. 

Memoires de 1' Academic des Sciences et Lettres : Section de la 

MMecine. Montpellier. 
1849 B.M.; Camb.U.; Dub.E.D.S.; Dub.B.I.A.; Edinb.B.S.t.; 

Oxon.B.; B.S. 
Eecueil des Bulletins publies par la Socie"te Libre des Sciences, etc., 

de Montpellier. Montpellier. 
180314. B.M.; Camb.U.; Oxon.B.t. 

\ Memorie della Begia Accademia di Scienze, Lettere ed Arti di 
/ Modena. Modena. 
1833 B.M.; Dub.B.I.A.t.; Dub.T.C.t.; Edinb.E.S.; Math.S.i.; 

N.H.M.; Oxon.B.t.; U.C.L.t. 

^Memorie di Matematica e di Fisica della Societa Italiana delle 
| Scienze. Modena. 
1782 B.M.t.; Camb.P.S.; Camb.U.t.; Dub.B.I.A.; Edinb.B.S.t.; 

Linn.S.t.; Oxon.B.t.; B.A.S.t.; B.S.; U.C.L.t. 
See Bm. 8. It. Mm., Verona Mm. 8. It. and Verona 8. It. Mm. 



Mod. S. Nt. At. 

Moigno An. Cosmos... 



Moigno Cosmos 

Mondes(les) 



Mon. Sc 

Mosc. Bll. 8. Nt. 



Mosc. Obs. A. 



Mosc. S. Nt. Bll. 

Mosc. S. Sc. Bll. 



Mosc. Un . Mm 

Mosc. TTn. Mm. (Ps.-Mth 



Mth. Oz 

Mth. Misc 

Mth. Nt. B. Ung. 



Mth. Term. Ets 

Mth. Termt. ts 

Mth. Ts 

Mulhousc Bll. 

Mulhouse Bll. S. In. 
Mulhouse 8. In. Bll. 

Munch. Ab 

Munch. Ak. Ab 



Munch. Sb. 



List of Serial Publications 

Atti della Societa dei Naturalisti di Modena. Modena. 
1883- Camb.U.; Dub.R.I.A.i.; N.H.M. 
.. Annuaire du Cosmos ; Moigno. Paris. 
185970. B.M. 

( Cosmos. Revue Encyclopedique Hebdomadaire des Progress des 
I Sciences: Moigno. Paris. 
' 1852 B.M.; Camb.U.; Dub.T.C.; Edinb.R.S.i.; N.H.M.i.; 

Oxon.B.; P.O.i ; R.A.S.i.; R.S. 
Le Moniteur Scientifique du Chimiste et du Manufacturier ; Quesne- 

ville. Paris. 

1857 B.M.; Chem.S.i.; Dub.R.C.S.i.; Oxon.B.; P.O.; R.A.S.i. 
Bulletin de la Societe Imperiale des Naturalistes. Moscou. 
1829 B.M. ; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.R.D.S.; 
Dub.R.I.A.; Edinb.R.S.i.; Glasg.U.i.;Linn.S.;N.H.M.;Oxon.B.i.; 
Oxon.R.; P.O.i.; R.A.S.i.; R.S. 
See Mosc. 8. Nt. Bll. 

Annales de 1'Observatoire de Moscou; Bredichin. Moscou. 
1874 B.M.i.; Camb.U.; R.A.S.; R.S. 
.. See Mosc. Bll. 8. Nt. 

.. Bulletin of the Imperial Society of Lovers of Natural Science, 
Anthropology and Ethnography, in connection with the Imperial 
University of Moscow. [In Russian.] Moscow. 
1865 B.M.i.; Edinb.R.S.i.; N.H.M.i. 

.. Scientific Memoirs of the Imperial University of Moscow. [In 
Russian.] Moscow. 

B.M.i.; Chem.S.i.; N.H.M.i. 
.) Scientific Memoirs of the Imperial University of Moscow. Section 

Phys.-Math. Moscow. 
188096. Chem.S. 
.. Mathematische Annalen ; Clebsch. Leipzig. 

1869 B.M.; Camb.P.S.; Camb.U.; Dub.N.L.I.i.; Dub.R.C.S.i.; 
Dub.R.D.S.i.; Dub.T.C.i.; Edinb.U.; Glasg.U.; Math.S.; Oxon.R.; 
R.S.; U.C.L. 
.. The Mathematical Gazette. London. 

1894 B.M.; Camb.U.; Math.S.; U.C.L.i. 
.. The Mathematical Miscellany; Gill. New York. 

183639. U.C.L. 
.. Mathematische und naturwissenschaftliche Berichte aus Ungarn. 

Berlin. 
1882 Camb.P.S.; Chem.S.; Edinb.R.S.; R.A.S.i.; R.S. 

(Mathematikai e"s termeszettudomanyi Ertesito. Kiadja a Magyar 
Tudomanyos Akademia. [Mathematical and Natural Science 
Report, published by the Hungarian Academy of Science.] Budapest. 
1883 B.M.i.; Edinb.R.S.; N.H.M.; R.S. 
.. Mathematisk Tidsskrift. Kjpbenhavn. 

1859 B.M.; Camb.U.; Oxon.B.; R.S.i. 
.. (Bulletin de la Societe Industrielle de Mulhouse. Mulhouse. 
.. J1828 B.M.i.; Camb.U.i.; Chem.S.i.; Dub.R.C.S.i.; Dub.T.C.i.; 
.. ( Glasg.P.S.i.; Glasg.U.i.; Oxon.B.i.; P.O. 

.. i Abhandlungen der mathematisch-physikalischen Classe der Konigl. 
.. { Bayerischen Akademie der Wissengchaften. Miinchen. 

1832 B.M. ; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.T.C.; 
Edinb.R.S.; Edinb.U.; Glasg.U.; Linn.S.; Oxon.B.; Oxon.R.; 
P.O.; R.A.S.i.; R.S. 
.. Sitzungsberichte der Mathematisch-Physikalischen Classe der K. B. 

Akademie der Wissenschaften zu Miinchen. Miinchen. 
1871 B.M. ; Camb.P.S.; Camb.U.; Chem.S.; Dub.T.C.; 
Edinb.R.S.; Glasg.U.i.; Linn.S.; Oxon.B.; Oxon.R.; P.O.; 
R.A.S.; R.S.; U.C.L.i. 
. . Denkschrif ten der Konigl. Bayerischen Akademie der Wissenschaften 

zu Miinchen. Miinchen u. Salzbach. 

180824. B.M.; Camb.P.S.; Camb.U.; N.H.M.; Oxon.R.; P.O.; R.S. 
.. Sitzungsberichte der Konigl. Bayerischen Akademie der Wissen- 
schaften zu Miinchen. Miinchen. 

186070. B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.R.D.S.i.; 
Dub.R.I.A.i. ; Dub.T.C.i. ; Edinb.R.S. ; Linn.S. ; N.H.M. ; 
Oxon.B.; P.O.i.; R.A.S.; R.S. 



List of Serial Publications 



Nap. Ac. Font. At.. 
Nap. Ac. Sc. Mm. . 



Nap. At. Ac. .. 
Nap. At. Ac. Sc. 
Nap. At. I. Inc. 



N. A. Mtn. Nouvelles Annales de Mathematiques. Paris. 

1842 B.M.; Camb.U.; Dub.T.C.; Edinb.U.; Glasg.U.; Math.S.i.; 

Oxon.B.(R.); R.S.; U.C.L.i. 
Nancy Mm. S. Sc. Memoires de la Societe [Royale] des Sciences, Lettres, et Arts de 

Nancy. Nancy. 
1833 B.M.; Camb.U. i.; N.H.M.i.; Oxon.B.; R.S.i. 

Nancy a. Sc. Bll Bulletin de la Societe des Sciences de Nancy. Nancy, Paris. 

1873 B.M.; N.H.M.; R.S. 

N. Antol. Sc Nuova Antologia di Scienze, Lettere ed Arti. Firenze e Roma. 

1866 B.M.; Dub.N.L.I.i.; N.H.M. 
Nap. Ac. At Atti della Reale Accademia delle Scienze e Belle Lettere; Sezione 

della Societa R. Barbonica. Napoli. 
181951. B.M. ; Camb.U.; Dub.R.D.S.; N.H.M.; Oxon.B.; 

R.A.S.i.; R.S. 
Atti della R. Accademia delle Scienze Fisiche e Matematiche. 

Napoli. 
186382; 1888 B.M. ; Camb.U.; Dub.R.I.A.; Edinb.R.S.; 

Glasg.U.i.; Linn.S.i.; Math.S.i.; N.H.M.; Oxon.B.i.; Oxon.R.; 

R.A.S.i.; R.S. 

See Nap. At. Ac. and Nap. At. Ac. Sc. 
Atti dell' Accademia Pontaniana di Napoli. Napoli. 
1832 B.M.; Camb.U.; Dub.R.D.S.i.; N.H.M.; R.S.i.; U.C.L.i. 
Memorie della R. Accademia delle Scienze, etc. Napoli. 
185257. B.M.; Camb.U.; Dub.R.D.S.; Edinb.R.S.; Linn.S. ; 

N.H.M.; Oxon.B.; Oxon.R.; R.A.S.; R.S. 
See Nap. Mm. Ac. Sc. 

I See Nap. Ac. At. 

Atti del Real Istituto d' Incorraggiamento alle Scienze Natural! di 

Napoli. Napoli. 
1811 B.M.; Camb.U.; Edinb.R.S.i.; N.H.M.; Oxon.B.; P.O.; 

R.S.i. 
See Nap. I. Inc. At. 

Nap. At. S. Font Atti della Societa Pontaniana di Napoli. Napoli. 

181047. B.M.; Camb.U.; N.H.M.; R.S. 
See Nap. S. Font. At. 

Nap. I. Inc. At See Nap. At. I. Inc. 

Nap. Mm. Ac. Sc See Nap. Ac. Sc. Mm. 

Nap. Ms Museo di Letteratura e Filosofia ; Gatti . Napoli . 

184262. B.M.; Oxon.B. 

Nap. Rd Rendiconto dell' Accademia delle Scienze Fisiche e Matematiche. 

Napoli. 

1862 Camb.U.; Dub.R.I.A.; Edinb.R.S.; Glasg.U.i.; Linn.S.i.; 
Math.S.; N.H.M.; Oxon.R.i.; P.O.; R.A.S.; R.S.; U.C.L.i. 

Nap. S. Font. At See Nap. At. S. Pont. 

N. Arch. Wisk Nieuw Archief voor Wiskunde . Amsterdam . 

1875 Camb.P.S.i.; Edinb.R.S.i.; Math.S. 

N. A. Sc. Nt Nuovi Annali delle Scienze natural!; Alessandrini, Bertoloni, 

Gherardi, e Ranzani. Bologna. 
183854. Camb.U.; N.H.M.; Oxon.B.i.; R.S. 
See Bologna N. A. 

N. Cim II Nuovo Cimento, Giornale di Fisica, Chimica e Storia Naturale. 

Pisa. 

1855 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Edinb.R.S.i.; 
N.H.M.; Oxon.R.i.; P.O.i.; R.S. 

Nebr. Un. Stud University Studies. Published by the University of Nebraska. 

Lincoln, Nebraska. 

1888 B.M.; Camb.P.S.; Camb.U.; Dub.R.I.A.; Edinb.R.S.; 
Oxon.B.; R.S. 

N. Eng. I. Mn. E. T Transactions of the North of England Institute of Mining Engineers. 

Newcastle-upon-Tyne. 
1852 B.M.; Camb.U.; Edinb.R.S.i.; Oxon.B.i.; P.O.i.; R.S. 

Neucn. Bll (Bulletin de la Societe des Sciences Naturelles de Neuchatel. 

Neuch. S. Sc. Bll \ Neuchatel. 

1844 B.M.i. ; Camb.U.; Dub.R.I.A.; Edinb.R.S.i.; N.H.M.; 
Oxon.B.i.; R.A.S.i.; R.S.i. 

NH. Rv The Natural History Review and Quarterly Journal of Science. 

London and Dublin. 



List of Serial Publications 



185460. B.M.; Camb.U.; Dub.K.D.S.; Dub.T.C.; Glasg.P.S.; 

Linn.S.; N.H.M.; Oxon.R.; P.O.; U.C.L.i. 
The Natural History Review; a Quarterly Journal of Biological 

Science. London. 



Nicholson J. 



Niort Mm. de r Athenee 
N. Jb. Mn 



N. Mg. Ntvd 

Vd. Skr. .. 



N. KB. 8. Nt. Mm. (Mth. 
W. 8. W. Ph. 8. T 

H. 8. W. B. 8. J 

N. 8. W. R. 8. T. . 



W. Ts. Mth 

Niirnb. Nt. Gs. Ab 

Nv. Archt. T 

N.-Vorp. Mt. 

IT. Y. Am. Mth. 8. Bll. 

W. V. Am. Mth. 8. T. 
IT. T. Mth. 8. Bll. . 



1861-65. B.M.; Camb.P.S.; Camb.U.; Dub.R.D.S. 

Edinb.R.S.; Glasg.P.S.; Glasg.U.; Linn.S.; N.H.M. 

Oxon.R.; P.O.; R.S. 
Journal of Natural Philosophy, Chemistry, and the Arts 



Dub.T.C. ; 
Oxon.B.i.; 



Nicholson. 



London. 
17971813. B.M. ; Camb.U.; Chem.S.i. ; Dub.R.I.A.i. ; Dub. 

T.C.i.; Edinb.R.S.; Edinb.U.; Glasg.P.S.i.; Glasg.U.; N.H.M.; 

Oxon.B.; Oxon.R.; P.O.; R.A.S.i.; R.S.; U.C.L. 
Memoires de 1'Athenee de Niort, Societ4 Libre des Sciences et des 

Arts du departement des Deux-Sevres. Niort. 
1808(9). B.M.; Oxon.B.; R.S.i. 
Neues Jahrbuch fur Mineralogie, Geologic und Palaontologie. 

Stuttgart. 
1833 B.M.; Camb.U.; Chem.S.i.; Dub.N.L.I.i.; Dub.R.D.S.i.; 

Geol.M.; N.H.M. ; Oxon.R.; R.S. 
Nyt Magazin for Naturvidenskaberne. Christiania. 
1838 Camb.U.i.; Edinb.R.S. i.; Linn.S.i.; N.H.M.; R.S. 
Det Kongelige Norske Videnskabersselskabs Skrifter i det 19de 

Aarhundrede. Kjabenhavn og Trondhjem. 

1817 B.M.; Camb.U.t.; Dub.T.C.i.; Edinb.R.S.i.; N.H.M.; R.S. 
See Thrond. Skr. 
Memoirs of the Mathematical Section of the New Russian Society 

of Naturalists. [In Russian.] Odessa. 
1878- B.M.i.; Dub.R.I.A.; Math.S.i.; R.S.i. 
Transactions of the Philosophical Society of New South Wales. 

Sydney. 
1866. Camb.P.S.; Camb.U.; Chem.S. ; Edinb.R.S.i.; Glasg.U.; 

Linn.S.; Oxon.B.; R.A.S.; R.S. 
Journal and Proceedings of the Royal Society of New South Wales. 

Sydney. 
1876 B.M. ; Camb.P.S. ; Camb.U. ; Chem.S.i. ; Dub.T.C. ; 

Edinb.R.S.i.; Geol.M.i.; Glasg.P.S. i.; Glasg.U.i.; Linn.S.i.; 

N.H.M.; Oxon.B.; Oxon.R.i.; P.O.i.; R.A.S.; R.S. 
Transactions of the Royal Society of New South Wales. Sydney. 
186775. B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.R.D.S.; 

Dub.R.I.A. ; Dub.T.C. ; Edinb.R.S.i. ; Glasg.U.i. ; N.H.M. ; 

R.A.S.; R.S. 

Nature: a weekly illustrated Journal of Science. London. 
1870 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.N.L.L; Dub. 

R.C.S. ; Dub.R.D.S. ; Dub.R.I.A. ; Dub.T.C. ; Edinb.R.S. ; 

Edinb.U.; Geol.M.; Glasg.P.S.; Glasg.U.i.; Linn.S.; Oxon.B.; 

Oxon.R.; P.O.; R.A.S.; R.S.; U.C.L. 
Nyt Tidsskrift for Mathematik. Kjabenhavn. 
1890 B.M.; Math.S.i. 
Abhandlungen der Naturhistorischen Gesellschaft zu Niirnberg. 

Niirnberg. 

1852 B.M.i.; Camb.U.; Dub.R.I.A.; N.H.M.; R.S.i. 
Transactions of the Institution of Naval Architects. London. 
1860 B.M. ; Camb.U.; Dub.R.I.A.; Edinb.U.; P.O.; R.S. ; 

U.C.L.i. 
Mittheilungen aus dem Naturwissenschaftlichen Vereine von Neu- 

Vorpommern und Rugen. Berlin. 

1869 B.M.; Camb.U.; Dub.R.D.S.; Dub.R.I.A.; N.H.M. 
Bulletin of the American Mathematical Society. New York. 
1895 B.M. ; Camb.P.S.; Camb.U.; Dub.T.C.; Edinb.R.S.; 

Edinb.U.; Glasg.P.S.; Glasg.U.; Math.S.; Oxon.B.; Oxon.R.; 

R.S.i. 
Transactions of the American Mathematical Society. Lancaster, 

Pa. and New York. 
1900 Camb.P.S.; Camb.U.; Dub.R.I.A.; Dub.T.C.; Edinb.R.S.; 

Edinb.U.; Glasg.U.; Math.S.; Oxon.B.; Oxon.R.; R.S. 
Bulletin of the New York Mathematical Society. New York. 
189294. B.M.; Camb.P.S.; Camb.U.; Edinb.R.S.; Glasg.P.S.; 

Math.S.; Oxon.B.; Oxon.R.; R.A.S. 

xxxvi 



List of Serial Publications 



N. Z.I.T 

Obs 

Oestr. Z. Brgw 

Oken Isis 

OPUBC. Mt. Fis 

Orv.-Termt. Ets. (Termt. 
Szak) 

Fadova Ac. At. e Mm. . . . 

Fadova Mm. Ac 

Fadova N. Sag 

Fadova Rv. Period. . . 



Palermo Ac. At 

Palermo At 

Palermo Cir. Mt. Rd. 



Palermo G. Sc. Nt. 



Falomba Rac. 



Far. A. Cons. . . 



Far. Ac. Sc. Mm. 



Far. A. EC. Norm. 



Far. An. Met 

Far. An. S. Met 

Far. A. Obs 



Transactions and Proceedings of the New Zealand Institute. 

Wellington. 
1868 B.M.; Camb.P.S.i. ; Camb.U. ; Dub.K.D.S.; Dub.K.I.A. ; 

Edinb.E.S.; Edinb.U.; Geol.M.i.; Glasg.P.S.i.; Linn.S.; N.H.M.; 

Oxon.B.; Oxon.E.; P.O.; B.S.; U.C.L.i. 

The Observatory. A monthly Eeview of Astronomy. London. 

1878 Camb.P.S.; Camb.U.; Dub.T.C.i.; Edinb.E.S.; Oxon.B.; 
P.O.; E.A.S. 

Oesterreichische Zeitschrift fiir Berg- und Hiittenwesen ; von Otto 
Freiherrn von Hingenau. Wien. 

1853 B.M.; P.O. 

Isis, oder Encyclopadische Zeitung; Oken. Jena. 

181748. B.M.i. ; Camb.U. ; Edinb.U. ; Linn.S.i. ; N.H.M. ; 
Oxon.B. (E.); B.S. 

Opuscoli matematici e fisici di diversi Autori. Milano. 

183234. E.S. 

Orvos-Termeszettudomanyi Ertesit6 a Kolozsvari Orvos-Termeszettu- 
domanyi Tarsulat es az Erdelyi Muzeum-Egylet Termeszettu- 

domanyi Szakosztalyanak [Medical and Natural History 

Proceedings of the Sections of the Klausenburg Medical and 
Natural History Society and of the Natural History Section of the 
Museum Association of Transylvania.] Kolozsvar [Klausenburg]. 

1879 N.H.M.; B.S.i. 

Atti e Memorie della E. Accademia di Scienze, Lettere ed Arti in 

Padova. Nuova serie. Padova. 
1885 Edinb.E.S.; N.H.M. 
Memorie dell' Accademia di Scienze, Lettere, ed Arti di Padova. 

Padova. 

1809. B.M.; Camb.U.; N.H.M.; Oxon.B.; E.S. 
Nuovi Saggi dell' Accademia di Scienze, Lettere, ed Arti di Padova. 

Padova. 
181783. B.M.i.; Camb.U.i.; Dub.E.I.A.i.; Dub.T.C.i.; Edinb. 

E.S.; N.H.M.; Oxon.B.i.; E.S.i. 
Eevista Periodica dei Lavori della I. E. Accademia di Scienze, Lettere, 

ed Arti di Padova. Padova. 
1851 B.M.; Edinb.B.S.i.; N.H.M.; E.S.i. 

( Atti dell' Accademia di Scienze, Lettere ed Arti di Palermo. Palermo. 
-11845 B.M.; Camb.U.i.; Dub.E.I.A.; Dub.T.C.; N.H.M.; Oxon. 
( B.i.; E.A.S.i.; E.S. 

Eendiconti del Circolo Matematico di Palermo. Palermo. 
1887 B.M. ; Camb.P.S.; Camb.U.; Dub.E.I.A.; Dub.T.C.; 

Math.S.; E.S. 
Giornale di Scienze natural! ed economiche, pubblicato per cura del 

Consiglio di Perfezionamento annesso al E. Istituto Tecnico di 

Palermo. Palermo. 

1865 B.M.; Camb.U.; Dub.E.D.S.i.; E.S. 
Eaccolta di Lettere, etc. intorno alia Fisica ed alle Mathematiche ; 

Palomba. Eoma. 
184548. B.M.i. 

Annales du Conservatoire des Arts et Metiers. Paris. 
1861 B.M.; Camb.U.; Glasg.P.S.i.; Oxon.B.; P.O.; E.S. 
See A. Cons. Arts et Met. 

M^moires de 1'Academie des Sciences de 1'Institut de France. Paris. 
1816 B.M.; Camb.U.; Dub.N.L.I.i.; Dub.E.D.S.i.; Dub.T.C.i.; 

Edinb.E.S. i. ; Edinb.U.; N.H.M.; Oxon.B.; Oxon.E.; P.O.i.; 

E.A.S.i.; E.S.; U.C.L. 
See Far. Mm. Ac. Sc. 

Annales scientifiques de 1'Ecole Normale Superieure. Paris. 
1864 B.M.; Camb.P.S.i.; Camb.U.; Dub.N.L.I.i.; Dub.E.C.S.i.; 

Dub.E.D.S.i.; Edinb.E.S.i. ; Edinb.U.i. ; Glasg.U.i. ; Oxon.B.; 

E.S. 

See Far. EC. Norm. A. 

^Annuaire de la Societe Meteorologique de France. Paris. 
{1849 B.M.; Camb.U.i.; Dub.T.C.i.; Edinb.E.S.i.; E.S.i. 
Annales de 1'Observatoire de Paris; memoires publiees par U. J. 

Le Verrier. Paris. 

xxxvii 



List of Serial Publications 



Far. A. Pon. Chauss. 



Par. BU. 8. Encour. 



Par. Bll. 8. Gg . 



Par. EC. Norm. A. 
Par. EC. PoL Cor. 



Par. EC. PoL J. 



Par. Og. 8. Bll 

Par. Ing. Civ. Mm. 



Par. J. EC. Pol. .. 
Par. Mm. Ac. Be. 
Par. Mm. de I'l. .. 



Par. Mm. Ing. Civ.. 
Par. Mm. Sav. Etr. 



Par. Mm. 8. Sav. 



Par. Obs. A. 

Par. Ob. A. (Mm.) 

Par. Poids et TO.es. PV. 



Par. 8. Amat . Tr. 



Par. 8. Ap. B1L 



18-55 B.M. ; Camb.U. ; Dub.N.L.I. ; Dub.T.C. ; Edinb.R.S. ; 

Oxon.B.; B.A.S.; B.S. 
See Par. Obs. A. and Par. Obs. A. (Mm.) 
Annales des Fonts et Chaussees. Me'moires et documents relatifs 

a 1'Art des Constructions et au Service de 1'Ingenieur. Paris. 
1831 B.M.; Camb.U.; Edinb.U.i.; Glasg.P.S.i.; Glasg.U.i.; 

P.O.; B.S.i. 
See A. Pon. Chauss. 
Bulletin de la Society d'Encouragement pour 1'Industrie Nationale. 

Paris. 
1802 Camb.U.; Dub.B.C.S.i.; Dub.T.C.i.; Edinb.B.S.i.; Glasg. 

P.S.i.; Oxon.B.; P.O.; E.S. 
Bulletin de la Socie'te de Geographic. Paris. 
1822 B.M.; Camb.U.; Dub.B.I.A.; Edinb.B.S.i.; N.H.M. ; 

Oxon.B.; B.S.; U.C.L.i. 
See Par. Og. 8. Bll. and Par. 8. Gg. Bll. 

Bulletin des Sciences de la Societe Philomathique de Paris. Paris. 
17911805; 181424; 1864 B.M.i.; Camb.U.; Dub.T.C.i.; 

Edinb.B.S.i.; Glasg.U.i.; Math.S.i.; N.H.M.; Oxon.B.i.; P.O.i.; 

E.A.S.i.; B.S.; U.C.L. 
See Par. 8. Pblm. B1L 
See Par. A. EC. Norm. 
Correspondance sur 1'Ecole Polytechnique, a 1'usage des Eleves de 

cette Ecole; Hachette. Paris. 
180816. B.M.i.; Oxon.B.; B.S.; U.C.L. 
Journal de 1'Ecole Polytechnique. Paris. 
1795 B.M. ; Camb.P.S. ; Camb.U. ; Dub.E.I.A. ; Dub.T.C. ; 

Edinb.B.S. ; Edinb.U. ; Glasg.P.S.i.; Glasg.U. ; Linn.S.i. ; 

Math.S.i.; Oxon.B.(B.); P.O.; B.A.S.i.; B.S.; U.C.L.i. 
See Far. J. EC. PoL 
See Far. Bll. 8. Gg. 
Memoires et Comptes Bendus des Travaux de la Societe des Ingenieurs 

Civils. Paris. 

1848 B.M.; Glasg.U.i.; P.O. 
See Far. Mm. Ing. Civ. 
See Par. Be. PoL J. 
See Par. Ac. Sc. Mm. 
Memoires de la Classe des Sciences mathematiques et physiques 

de 1'Institut. Paris. 
17981815. B.M.; Edinb.B.S.; N.H.M. ; Oxon.B.; Oxon.B.; 

P.O.; B.A.S.i.; U.C.L. 
See Par. Ing. Civ. Mm. 
Memoires presentes a 1'Institut des Sciences, Lettres et Arts par 

divers Savans, et lus dans ses Assemblies : Sciences Mathematiques 

et Physiques. Paris. 
180611. B.M.; Camb.U.; Dub.B.D.S.; Dub.T.C.; Edinb.E.S.; 

N.H.M.; Oxon.B.; P.O.; E.A.S.; E.S.; U.C.L. 
Memoires presentes par divers Savans a l'Acad6mie des Sciences de 

1'Institut de France. Paris. 
1827 B.M. ; Camb.U.; Dub.T.C.; Edinb.E.S.i. ; Linn.S.i.; 

N.H.M.; Oxon.B.; Oxon.E.; P.O.i.; E.A.S.i.; E.S. 
Memoires des Societ^s Savantes et Litteraires de la Be"publique 

Francaise. Eecueillis et redige"s par les Citoyens Prony, etc. 

Paris. 
180102. B.M.; Oxon.B.; E.S. 

See Par. A. Obs. 

Comit^ International des Poids et Mesures. Proces-Verbaux des 

Seances. Paris. 
1875 Camb.P.S.; Camb.U.i.; Dub.B.D.S.; Oxon.E.; P.O.; 

E.A.S.; E.S. 
Notices des Travaux de la Society des Amateurs des Sciences 

physiques et naturelles de Paris. Paris. 
180708. 

-See Par. Tr. 8. Amat. 

Bulletin de la Societe d'Anthropologie de Paris. Paris. 
1860 B.M.; Camb.U.; Dub.E.I.A.; Edinb.E.S.i.; N.H.M.i.; 

Oxon.E.; E.S. 

xxxviii 



Far. Se. EC. Norm. 



Far. 8. Gg. Bll. . 
Far. 8. Mth. Bll. 



Par. 8. Fhlm. Bll 

Far. 8. Phlm. Mm. Cent. 



Far. 8. Fhlm. N. Bll. 



Far. 8. Fnlm. PV 



Far. T. Nauk Sc. Fam. . . 

Par. Tr. 8. Amat 

Perpignan. Bll. 8. Ag. 
Fyr. Orient 

Peterm. Mt. ... 



Phil. Trans 



Ph. Mg 



Phm. J 



Pisa A. Scuola Norm. 



Pisa A. Tin. Tosc 

Pisa A. Un. Tosc. Sc. 



Pisa N. O 

Pisa 8. Tosc. At. (PV.) .. 

Pistoja At. Ac 

Fogg. A 

-PoHgrafo 



List of Serial Publications 

Seances des Ecoles Normales. Paris. 

180001. R.S.; U.C.L. 

See Par. Bll. 8. Gg. and Par. Gg. 8. Bll. 

Bulletin de la Societe Mathematique de France. Paris. 

1873 B.M. ; Camb.P.S. ; Camb.U. ; Edinb.E.S. ; Math.S. ; 

Oxon.E.; E.A.S.; B.S. 
See Far. Bll. 8. Fhlxn. 
Memoires publics par la Soci^te" Philomathique a 1'occasion du 

Centenaire de sa Fondation. Paris. 
1888. B.M.; Edinb.E.S.; N.H.M.; E.A.S.; E.S. 
Nouveau Bulletin des Sciences de la Societe Philomathique de Paris. 

Paris. 
18071813; 182526; 183233. B.M.i.; Camb.U.; Dub.T.C. ; 

N.H.M.; P.O.i.; E.S.; U.C.L. 
Extraits des Proces-Verbaux des Seances de la Societe Philctaathique. 

Paris. 

183663. N.H.M.; E.S. 

Pamie,tnik Towarzystwa Nauk Scisiych w Paryzu. Paris. 
187182. B.M.; N.H.M. 
See Par. 8. Axnat. Tr. 
[Bulletin de la] Societe Agricole, Scientifique, et Litteraire des 

Pyrene'es-Orientales. Perpignan. 
1834 N.H.M. ; E.S.i. 
Mittheilungen aus Justus Perthes' Geographischer Anstalt iiber 

wichtige neue Erforschungen auf dem Gesammtgebiete der 

Geographic ; Petermann. Gotha. 
1855 B.M. ; Camb.U.; Dub.E.C.S.; Geol.M.i.; Glasg.P.S.i.; 

Glasg.U.; N.H.M.i.; Oxon.B. ; Oxon.E.; E.S.; U.C.L.i. 
Philosophical Transactions of the Eoyal Society of London. 

London. 
1665 B.M.; Camb.P.S. i. ; Camb.U.; Chem.S.i.; Dub.E.C.S.; 

Dub.E.I.A.; Dub.T.C.; Edinb.E.S.; Edinb.U.; Geol.M.; Glasg. 

P.S. ; Glasg.U.i.; Linn.S.i.; Math.S.i.; N.H.M.; Oxon.B.; 

Oxon.E.; P.O.; E.A.S.i.; E.S.; U.C.L.i. 
The London, Edinburgh, and Dublin Philosophical Magazine and 

Journal of Science. London. 
1827 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.E.D.S.; Dub. 

E.I.A.; Edinb.E.S.; Edinb.U.; Geol.M.i.; Glasg.P.S.i.; Glasg.U.; 

Linn.S.i.; Math.S.i.; N.H.M.; Oxon.B.; Oxon.E.; P.O.; E.A.S.; 

E.S.; U.C.L. 

The Pharmaceutical Journal and Transactions. London. 
1841 B.M.; Camb.U.; Chem.S.; Dub.N.L.I.i. ; Dub.T.C.i.; 

Glasg.P.S.; Glasg.U.i.; N.H.M.; Oxon.B.; Oxon.B. (E.) ; E.S.i.; 

U.C.L. 
Philosophische Studien herausgegeben von Wilhelm Wundt. 

Leipzig. 

1883 Camb.U.; Dub.T.C.; Edinb.U.; Oxon.B.; E.S.; U.C.L. 
Annali della E. Scuola Normale Superiore di Pisa. Scienze Fisiche 

e Matematiche. Pisa. 
1871. Oxon.B.; Oxon.E.; E.S. 

1 Annali delle Universita Toscane. (Parte 2da.) Scienze Cosmo- 
logiche. Pisa. 
1846 Camb.U.i.; N.H.M.; E.S.i. 
Nuovo Giornale de' Letterati. Pisa. 
182239. B.M.; Camb.U.; Oxon.B. 
Atti della Societa Toscana di Scienze Natural! residente in Pisa. 

Process! Verbali. Pisa. 

1875 B.M.; Camb.P.S.i.; Dub.T.C.; N.H.M.; E.S. 
Atti della E. Accademia Pistojese di Scienze, Lettere, ed Arti: 

Memorie di Matematica e Fisica, per 1' anno 1816. Pistoja. 
1816. B.M.; Camb.U.; N.H.M.; Oxon.B.; E.S. 
Annalen der Physik und Chemie ; Poggendorff. Leipzig. 
1824 B.M. ; Camb.P.S.i.; Camb.U.; Chem.S.; Dub.E.I.A.; 

Dub.T.C.; Edinb.E.S.; Edinb.U.; Glasg.P.S.i.; Glasg.U. i.; 

N.H.M.; Oxon.B.(E-); P.O.; E.S.; U.C.L.i. 
See A. Ps. C. 

II Poligrafo: Giornale di Scienze, Lettere, ed Arti; Orti. Verona. 
183045. B.M.; Oxon.B. 

xxxix 



Pop. As. 

Frace Mt.-Flr 

PragAb 



Prag Cesk6 Ak. Fr. Jos. 



Prag Ceske Ak. Fr. Jos. 



Prag Fr. Jos. Ac. sc. mi. 

(JlftTi. Nt.) 



Frag Jb. Bohm. Ms 

Prag Sb 



Presse Sc 

Ps. Kv. .. 



Ps. Z. 



List of Serial Publications 

Poly tech nische Mittheilungen, unter Mitwirkung von Professoren 

hoherer technischer Lehranstalten. Tubingen. 
184446. B.M.; B.S. 

Popular Astronomy. Northfield, Minnesota. 
1894 B.M.; Glasg.U.; K.A.S. 
Prace Matematyczno-Fizyczne. Warsaw. 
1888 Camb.P.S.; Camb.U.; Chem.S.i.; Dub.B.I.A.i.; Math.S.; 

E.S.i. 
Abhandlungen der k. Bohmischen Gesellschaft der Wissenschaften. 

Prag. 
180492. B.M.i.; Camb.P.S.; Camb.U.i.; Dub.E.I.A.i.; Edinb. 

E.S.i.; Linn.S.i.; N.H.M.; Oxon.B.; E.S.i. 
See Bohm. Os. Ab. 
Pamatnik na oslavu padesatileteno panovnickeho jubilea Jeho 

veliCenstva cisafe a krale Frantiska Josef a I. Vydala Ceskii 

Akademie Cisafe Frantiska Josefa pro Vedy, Slovesnost a Umeni. 

[Memoirs in honour of the jubilee of his Imperial and Eoyal 

Majesty Franz Joseph I. Edited by the Imperial Bohemian 

Franz- Joseph Academy of Sciences, Literature and Art.] Praze. 

(Prag.) 

1898. Camb.P.S.; N.H.M. 
Eozprawy Ceske Akademie Cisafe Frantiska Josefa Pro Vedy, 

Slovesnost a UmSni. [Memoirs of the Imperial Bohemian Franz - 

Joseph Academy of Sciences, Literature and Art.] Prag. 
1891 B.M.; Edinb.B.S.; N.H.M.i. 
Academic des Sciences de 1'Empereur Francois Joseph I (Ceska 

Akademie Cisafe Frantiska Josefa I). Bulletin International. 

Eesum6 des Travaux pre'sentes. Sciences Mathematiques et 

Naturelles. Prag. 
1897 Edinb.E.S.; N.H.M.i. 
Jahrbiicher des Bohmischen Museums fur Natur- und Landerkunde, 

etc. Prag. 

183031. B.M.; N.H.M. 
Sitzungsberichte der k. Bohmischen Gesellschaft der Wissenschaften 

in Prag. Prag. 
1859 Camb.P.S.; Camb.U.i.; Dub.E.D.S.; Dub.E.I.A.; Edinb. 

E.S.i.; Linn.S.i.; N.H.M.; E.S.; U.C.L.i. 
Presse Scientifique des Deux Mondes. Paris. 
186066. B.M.; E.S.i. 

The Physical Be view. New York, London, Berlin. 
1894 B.M.; Camb.P.S.; Camb.U.; Dub.E.C.S.; Edinb.E.S.; 

Edinb.U.i.; Oxon.E.; P.O.; B.S. 
Physikalische Zeitschrift. Leipzig. 
1899 Camb.P.S.; Edinb. U.; Oxon.E.; E.S. 



Queb. T 

Queb. T. Lt. 8 



Quetelet Cor. BXth. . 
QJ. 



QJ. Be. 



{ Transactions of the Literary and Historical Society of Quebec. 

Quebec. 

1829 B.M.i.; Dub.E.I.A.; Edinb.B.S.i.; Glasg.P.S.i.; Linn.S.i.; 
[ N.H.M.; B.S.i. 
Correspondance Mathematique et Physique; publi^e par MM. 

Gamier et Quetelet. Gand et Bruxelles. 
182539. B.M.; Camb.U.; E.A.S.i.; E.S.; U.C.L. 
The Quarterly Journal of Pure and Applied Mathematics. London. 
1855 B.M.; Camb.P.S.; Camb.U.; Dub.N.L.L; Dub.T.C. ; 

Edinb.B.S.i.; Edinb.U. ; Glasg.P.S.i.; Glasg.U.; Math.S.i. ; 

Oxon.B.; Oxon.B.; P.O.; B.A.S.i.; E.S.; U.C.L. 
The Journal of Science and the Arts ; edited at the Eoyal Institution 

of Great Britain. London. Continued as : Quarterly Journal of 

Science, Literature and Arts. London. 
181630. B.M.; Camb.U.; Chem.S.; Dub.T.C.; Edinb.E.S.; 

Glasg.U.; Oxon.B.; Oxon.E.; E.S.; U.C.L. 



Railroad & Bng. J The Bailroad and Engineering Journal. New York. 

188792. B.M.; P.O. 
Ranuzzi An. Og Annuario geografico Italiano ; Banuz z i . Bologna . 

184445. B.M.; Camb.U. 

xl 



List of Serial Publications 



Bee. Mth. (Moscou) ... 

R, E. Pp 

Rheinl. Westphal. Sb. 

Riga Cor.-Bl. 

B. I. J 

Bio Arch. Falestr 

B. I. P. .. 



Bm. At 

Bm. At. IV. Line. 



Im. At. B. Ac. 



Bm. Cor. Sc 



Bm. Mm. Osserv. 



Bm. N. Line. At. . . . 
Bm. IT. Line, Mm. 



Bm. B. Ac. Line. At. ... 
Bm. B. Ac. Line. Mm. 



Bm. B. Ac. Line. Bd. 



Bm. B. Ac. Line. T 



Bm. S. Cor 

Bm. S. It. Mm. . . 



Rochester (W. Y.) Ac. 
Sc. P.... 



Bot. N. Vh. 



Kecueil mathematique. Publie par la Societe Mathematique de 

Moscou. [In Eussian.] Moscou. 
1866 R.S. 
Papers on subjects connected with the duties of the Corps of Royal 

Engineers. London. 

1844 Camb.U.; Geol.M.i.; Glasg.U.i.; P.O.i. 
Sitzungsbericht des Naturhistorischen Vereins der Preussischen 

Rheinlande und Westphalens. Bonn. 
1844 Dub.R.D.S.i. ; Dub.R.I.A.i. ; Edinb.R.S.; Linn.S.i.; 

N.H.M.; Oxon.R.; R.S.i. 

Correspondenzblatt des Naturforscher- Vereins zu Riga. Riga. 
1846 B.M.; Dub.R.I.A.i.; N.H.M.; R.S.i. 
Journal of the Royal Institution of Great Britain. London. 
180203; 183031. Camb.U.i.; Chem.S.i.; Dub.R.D.S.; Edinb. 

R.S.i.; Glasg.P.S.i.; Linn.S.i. ; N.H.M.i. ; Oxon.R.; P.O.i.; 

R.A.S.i.; R.S.; U.C.L.i. 

Archives da Palestra Scientifica do Rio de Janeiro. Rio de Janeiro. 
1858. N.H.M.; R.S. 
Notice of the Proceedings at the meetings of the members of the 

Royal Institution, with Abstracts of the Discourses delivered at 

the Evening Meetings. London. 
1851 B.M. ; Camb.U. ; Chem.S. ; Dub.R.I.A. ; Dub.T.C. ; 

Edinb.R.S.; Geol.M.; Glasg.P.S.; Glasg.U.; Linn.S.; N.H.M.; 

Oxon.R.; P.O.; R.A.S.; R.S.; U.C.L. 
(Atti dell' Accademia Pontificia dei Nuovi Lincei. Roma. 
- 1 1847 B.M. ; Dub.R.I.A. ; Edinb.R.S. ; N.H.M. ; Oxon.B.i. ; 
( R.A.S.i.; R.S. 
See Bm. N. Line. At. 

Atti della Reale Accademia dei Lincei. Roma. 
187083. B.M.; Camb.P.S.; Camb.U.i.; Chem.S.i.; Dub.R.D.S.; 

Dub.R.I.A.; Linn.S.; Math.S.; N.H.M.; Oxon.B. ; Oxon.R.i.; 

R.A.S.i.; R.S.; U.C.L.i. 
See Bm. B. Ac. Line. At. 
Corrispondenza Scientifica in Roma per le avanzamento delle 

Scienze, etc. Roma. 
1848 

See Bm. S. Cor. 
Memorie dell' Osservatorio dell' Universita Gregoriana del Collegio 

Romano, diretto dai PP. della Compagnia di Gesu. Roma. 
185063. B.M.; R.A.S.; R.S. 
See Bm. At. ".,,,/ Bm. At. N. Line. 

Memorie della Pontificia Accademia dei Nuovi Lincei. Roma. 
1887 Dnb.R.D.S.; Dub.R.I.A.; Edinb.R.S.; N.H.M.; R.S. 
See Bm. -*t. B. Ac. 
Atti della R. Accademia dei Lincei. Memorie della Classe di Scienze 

fisiche, matematiche e naturali. Roma. 
1877 B.M.i.; Camb.P.S.; Camb.U.; Chem.S.; Dub.R.I.A.i. ; 

Edinb.R.S.; Glasg.P.S.i.; Glasg.U.i.; Linn.S.; Math.S.; N.H.M.; 

Oxon.B.; Oxon.R.; P.O.i.; R.A.S.; R.S.; U.C.L. 
Atti della R. Accademia dei Lincei. Rendiconti. Roma. 
1885 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.T.C.; Edinb. 

R.S.; Glasg.U.i.; Linn.S.; Math.S.; N.H.M.; Oxon.B.; Oxon.R.; 

R.A.S.; R.S.; U.C.L. 

Atti della R. Accademia dei Lincei. Transunti. Roma. 
187784. B.M. ; Camb.P.S.; Camb.U.; Chem.S.; Dub.R.I.A.; 

Edinb.R.S.; Glasg.P.S.i.; Linn.S.; Math.S.; N.H.M.; Oxon.B.- 

Oxon.R.; R.A.S.; R.S.; U.C.L. 
See Bm. Cor. Sc. 
Memorie di Matematica e di Fisica, della Societa Italiana delle 

Scienze. Napoli e Roma. 
1782 B.M.i.; Camb.P.S.; Camb.U.i.; Dub.R.I.A.; Edinb.R.S.i.- 

Linn.S.i.; Oxon.B.i.; R.A.S.i.; R.S.; U.C.L.i. 
See Mod. Mm. S. It., Verona Mm. S. It. and Verona 8. It. Mm. 
Proceedings of the Rochester Academy of Sciences. Rochester, N.Y. 
1890 B.M.; Camb.P.S.; Edinb.R.S.i.; Linn.S.; N.H.M.; R.S.; 

U.C.L.i. 
Nieuwe Verhandelingen van het Bataafsch Genootschap der Proefon- 

dervindelijke Wijsbegeerte te Rotterdam. Rotterdam. 

xli 



List of Serial Publications 

1800 B.M.f.; Camb.U.i.; Chem.S.i.; Dub.E.D.S.; Edinb.K.S.i.; 
Oxon.B.; B.S. 

Rouen Bll. 8. Em Bulletins [des travaux] de la Societe Libre d'Emulation de Kouen. 

Rouen. 

1837 B.M.; Oxon.B. 

Rouen Ac. Tr. \ Precis analytique des Travaux de 1' Academic des Sciences, Belles- 
Rouen Tr. Ac. . I Lettres, et Arts de Bouen. Bouen. 

1804 B.M. ; Camb.U. ; Dub.B.I.A. ; Dub.T.C. ; N.H.M.i. ; 

Oxon.B.; B.S.i. 

Rpxn. Mth Bepertorium der literarischen Arbeiten aus dem Gebiete der reinen 

und angewandten Mathematik. Leipzig. 
187779. Camb.U.; B.S. 

Rpm. PB. Bepertorium der Physik. Enthaltend eine vollstandige Zusammen- 

stellung der neuern Fortschritte dieser Wissenschaft. Berlin. 
183749. Chem.S.; Glasg.P.S.i.; P.O.; B.S.; U.C.L. 

Rs. Qg. Gs. D Denkschrif ten der Bussischen Geographischen Gesellschaf t zu 

St Petersburg. Weimar. 
1849. B.M.; Camb.U.; B.S. 
R S P Proceedings of the Boyal Society of London. London. 

1832 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.N.L.I.i. ; 
Dub.B.C.S.; Dub.B.D.S.; Dub.B.I.A.; Dub.T.C.; Edinb.B.S.; 
Edinb.U.; Geol.M.; Glasg.P.S.; Glasg.U.i.; Linn.S.i.; Math.S.i.; 
N.H.M.; Oxon.B.i.; Oxon.B.; P.O.; B.A.S.; B.S.; U.C.L. 

Rs. Ps.-C. S. J Journal of the Bussian Physico-Chemical Society of the Imperial 

University of St Petersburg. [In Bussian.] St Petersburg. 
1869 Camb.P.S.i.; Chem.S.; Edinb.B.S.i.; N.H.M. 

R. 8. Yearbook Yearbook of the Boyal Society of London. (Biography. 1900.) 

Rv. Artl. Bevue d'Artillerie. Paris, Nancy. 

1872 B.M.; P.O. 

Rv. Brazil. Bevista Brazileira, Jornal de Sciencias, Lettras, e Artes; Oliveira. 

Bio de Janeiro. 
185761. B.M.; N.H.M.; B.S.i. 

Rv. Cours. Se Bevue des Cours Scientifiques de la France et de 1'Etranger; Eug. 

Yung et Em. Alglave. Paris. 

1863-70. B.M.; Edinb.B.S.i.; Edinb.U.; N.H.M. ; Oxon.E. ; 
P.O.; B.S. 

Rv. Ligure Bivista Ligure, giornale di Lettere, Scienze, etc. Geneva. 

1843. B.M.; N.H.M.; Oxon.B. 

Rv. Mar IBevue maritime et coloniale. Paris. 

Rv. Mar. et Col J1861 B.M.; Oxon.B.; Oxon.B.; P.O. 

Rv. Mt. Bivista di Matematica. Torino. 

189195. Camb.U.; Oxon.B.; E.S. 

Rv. Mtb Bevue de Mathematiques. (Bivista di Matematica.) Turin. 

1896 Camb.U.; Oxon.B.; Oxon.B.; B.S. 

Rv. Be La Revue Scientifique de la France et de 1'Etranger. Paris. 

1871- B.M.; Camb.U.; Edinb.B.S.; Edinb.U.; N.H.M.; Oxon.B,; 
P.O.; B.A.S.i.; B.S. 

Rv. Sc.-lnd Bivista Scientifico-Industriale delle principali scoperte ed invenzioni 

fatte nelle scienze e nelle Industrie. Firenze. 
1869- P.O. 

Rv. Un. Mines Bevue Universelle des Mines , de la Metallurgie , etc . Lie"ge & Paris . 

1857 B.M.; Camb.U.; Dub.B.I.A.i.; Glasg.P.S.i.; Glasg.U.i.; 

N.H.M.; P.O. 
See Cuyper Rv. Tin. 



The Transactions of the South African Philosophical Society. Cape 

Town. 

1878 B.M.; Camb.P.S.; Camb.U.i.; Chem.S.; Edinb.B.S.; 
Edinb.U.; Glasg.P.S.; Linn.S.i.; N.H.M.; Oxon.B.; Oxon.R.; 
P.O.; B.A.S.; B.S. 

s. Afr. QJ. The South African Quarterly Journal; edited at the African Insti- 
tution. Cape Town. 

183035. B.M.i.; Edinb.B.S.i.; N.H.M. 

Santiago de Chile Un. A. Anales de la Universidad de Chile. Santiago de Chile. 
1843 B.M.i.; Dub.T.C.; N.H.M.i.; Oxon.B.i. 
See Chile A. Un. 

SartheS. Bll Bulletin de la Societe d' Agriculture, etc., de la Sarthe. Le Mans. 

1833 B.S.i. 

xlii 



List of Serial Publications 

S. Aust. R. a. T Transactions and Proceedings and Eeport of the Royal Society of 

South Australia. Adelaide. 

1877 Camb.P.S.i.; Camb.U.i.; Chem.S.i.; Dub.E.I.A.i.; Edinb. 
E.S.; Linn.S.i.; N.H.M.; P.O.; E.A.S.; B.S.i. 

Sav. Ac. Mm ( Memoires de la Societe Academique de Savoie. Chambery. 

Sav. Mm. Ac /1825 Camb.U.; Dub.E.I.A.; Dub.T.C.; N.H.M.; Oxon.B.; E.S.i. 

See Chambery Ittm. Ac. Sav. 

Sc. Abs Science Abstracts. Physics and Electrical Engineering. London. 

1898 Camb.P.S.; Camb.U.; Chem.S.; Edinb.E.S.i.; Edinb.U.; 
Glasg.P.S.; Oxon.E.; P.O.; E.A.S.i.; E.S.; U.C.L. 

Sch. Gs. KT. D Neue Denkschriften der allgemeinen Schweizerischen Gesellschaft 

fiir die gesammten Naturwissenschaften. Neuchatel, Zurich, etc. 
1837 B.M.; Camb.P.S.; Camb.U.; Dub.E.D.S.i.; Dub.B.I.A.i.; 

Edinb.E.S.; Linn.S.i.; N.H.M.; Oxon.B.; E.S. 
See Zur. N. D. Sch. Gs. 

Sch. Gs. Vh Verhandlungen der Schweizerischen Gesellschaft fiir die gesammten 

Naturwissenschaften. Aarau, etc. 

1823 B.M.i.; Edinb.E.S.i.; Linn.S.i.; N.H.M.; E.S. 
See Sch. Nf. Gs. Vb. 

Schlomilch Z Zeitschrif t fiir Mathematik und Physik ; Schlomilch. Leipzig. 

1856 B.M.; Camb.U.; Dub.N.L.I.i.; Dub.E.D.S.i.; Dub.B.I.A.i.; 
Dub.T.C.i.; Edinb.U.; Glasg.U.i.; Math.S.i.; Oxon.B. (E.); E.S.; 
U.C.L.t. 
See Z. Mth. Ps. 

Sch. Nf. Gs. Vh See Sch. Gs. Vh. 

Schumacher As. Ab Astronomische Abhandlungen ; Schumacher. Altona. 

182325. B.M.; Camb.U.; Dub.E.D.S.; Edinb.E.S.; E.A.S.; E.S. 

Schweigger J Journal fiir Chemie und Physik ; Schweigger. Niirnberg. 

181129. Edinb.E.S.; N.H.M.; Oxon.E.; P.O. Continued as: 
Neues Jahrbuch der Chemie und Physik ; Schweigger-Seidel. Berlin. 
183133. B.M.; Chem.S.; Edinb.E.S.; N.H.M.; Oxon.E.; P.O.; 
E.S. 

Science. Cambridge, Mass. , and New York. 

1883 B.M. ; Dub.N.L.I.i.; Dub.E.C.S.i. ; Edinb.E.S.; Edinb. 
U.i.; Glasg.P.S.i.; N.H.M.; Oxon.E.i.; P.O.; E.A.S.i. 

Transactions of the Eoyal Scottish Society of Arts. Edinburgh. 

1841 B.M.t.; Camb.U.; Dub.E.D.S.; Edinb.E.S.; Edinb.U.; 

Glasg.P.S.; Glasg.U.; P.O.; E.S. 
See Edinb. Sc. S. Arts T. and Edinb. T. Sc. S. Arts. 

Sid. Mess The Sidereal Messenger. Northfield, Minn. 

188391. B.M.; E.A.S. 

Siena At. Ac Atti deL' Accademia delle Scienze di Siena detta de' Fisio-critici. 

Siena. 

1761 B.M.; Camb.U.i.; Dub.E.I.A.i.; Dub.T.C.i.; N.H.M.t.; 
Oxon.B.; E.S.i. 

The American Journal of Science and Arts ; Silliman. New Haven. 

1818 B.M.; Camb.P.S.i.; Camb.U.; Chem.S.i.; Dub.N.L.I.i.; 
Dub.E.C.S.i.; Dub.T.C.i.; Edinb.E.S.; Edinb.U.; Geol.M.; 
Glasg.P.S.; Glasg.U.i.; N.H.M.; Oxon.B.; Oxon.E.; P.O.; 
E.A.S.i.; E.S. 
See Am. J. Sc. 

Skandia. Tidskrift for Vetenskap och Konst; utgifven af Svenska 

Litteratur-Foreningen. Upsala. 
183337. B.M. 

IForhandlingar vid det af Skandinaviska Naturforskare och Lakare 
hallna Mote Gotheborg, etc. 
1839 Oxon.B.i.; E.S.i. 
Forhandlingerne ved de Skandinaviske Naturforskeres...Mfde.... 
Gotheborg, etc. 
1839 B.M.; N.H.M.; E.S.i. 

Smiths. Ct Smithsonian Contributions to Knowledge. Washington. 

1848 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.T.C.; Edinb. 
E.S. ; Edinb.U.; Geol.M. i. ; Glasg.P.S.; Glasg.U.i.; Linn.S. ; 
N.H.M.; Oxon.B.; Oxon.B.i.; P.O.i.; E.A.S.; E.S.; U.C.L.i. 

Smiths. Misc. Col Smithsonian Miscellaneous Collections. Washington. 

1862 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.T.C.; Edinb. 
E.S. ; Edinb.U.; Geol.M.; Glasg.P.S.; Glasg.U.; Linn.S.; 
N.H.M.; Oxon.B.; Oxon.E.i.; P.O.i.; E.A.S. ; E.S.; U.C.L.i. 



List of Serial Publications 



Spet. It. 

Steierm. Mt. 



smiths. Rp Annual Report of the Board of Regents of the Smithsonian Insti- 
tution. Washington. 

1846 B.M.i.; Camb.P.S.; Camb.U.; Dub.T.C.; Edinb.R.S.i.; 
Geol.M.; Glasg.P.S.i.; Glasg.U.; Linn.S.i.; Math.S.i.; N.H.M.i.; 
Oxon.B.; Oxon.R.i.; P.O.i.; R.A.S.i.; R.S.i.; U.C.L.i. 
Memorie della Societa degli Spettroscopisti Italian!, raccolte e 

pubblicate per cura del Prof. P. Tacchini. Palermo. 
1872 B.M.i.; Camb.U.; Edinb.R.S.i.; P.O.; R.A.S.; R.S. 
Mittheilungen des Naturwissenschaftlichen Vereins fur Steiermark. 

Graz. 
1863 B.M.; Camb.U.i.; Dub.R.I.A.; Edinb.R.S.i.; Linn.S.i.; 

N.H.M.; R.S.; U.C.L.i. 

... Bericht iiber die Thatigkeit der St. Gallischen Naturwissenschaft- 
lichen Gesellschaft. St. Gallen. 
I860 N.H.M.; R.S.i. 

... The Transactions of the Academy of Science of St. Louis. St. Louis. 
1856 B.M.; Dub.R.I.A.; Edinb.R.S.; Glasg.P.S.; Linn.S.i.; 

N.H.M.; Oxon.B.; P.O.i.; R.S. 

(Kongliga Svenska Vetenskaps-Akademiens Handlingar. Stockholm. 
"-1 1739 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.R.I.A.; 
( Edinb.R.S.i.; Glasg.P.S.i.; Linn.S.i.; N.H.M.; R.A.S.; R.S. 
.. Bihang till Kongl. Svenska Vetenskaps-Akademiens Handlingar. 

Stockholm. 

1872 B.M. ; Camb.P.S.; Camb.U.; Chem.S.; Dub.R.I.A.; 
.. Edinb.R.S.; Glasg.P.S.; Linn.S.i.; N.H.M.; R.A.S.; R.S. 
.. Ofversigt af Kongl. Vetenskaps-Akademiens Forhandlingar. Stock- 
holm. 

1844 B.M. ; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.R.I.A.; 
Edinb.R.S.i.; Glasg.P.S.i.; Glasg.U.i.; Linn.S.i.; N.H.M.; 
Oxon.R.; R.A.S.; R.S.; U.C.L.i. 
.. Lefnadsteckningar ofver Kongl. Svenska Vetenskaps Akademien... 

ledamSter. Stockholm. 
186973. Chem.S.i.; Dub.R.I.A.; Edinb.R.S.; Glasg.P.S.; 

Linn.S.i.; R.A.S.; R.S. 
. . Memoires de 1'Academie Imperiale des Sciences de St. Petersbourg. 

St. Petersbourg. 

1803 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.R.D.S.; 
Dub.R.I.A.; Dub.T.C.; Edinb.R.S.; Edinb.U. ; Glasg.U.i.; 
N.H.M.; Oxon.B.; Oxon.R.; P.O.i.; R.S.; U.C.L.i. 
See St. Pet. Ac. Sc. Mm., St. Pet. Mm. and St. Pet. Mm. Ac. Sc. 
.. Bulletin Scientifique public par 1'Academie Imperiale des Sciences 

de St. Petersbourg. St. Petersbourg. 
183642. 
Bulletin de la Classe Physico-mathematique de 1'Academie Imperiale 

des Sciences de St. Petersbourg. St. Petersbourg and Leipzig. 
1843-59. 

Bulletinde 1'Academie des Sciences de St.Petersbourg. St.Petersbourg. 
1860 B.M.i.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.R.I.A.; 
Edinb.R.S.; Glasg.P.S.i.; Glasg.U.; Linn.S.i.; N.H.M.; Oxon.B.; 
Oxon.R.i.; P.O.i.; R.A.S.i.; R.S. 
See St. Pet. Bll. Ac. Sc. and St. Pet. Bull. Sc. 
.. See St. Pet. Ac. Mm. 
.) Memoirs of the Imperial Academy of Science. [In Russian.] 

St. Petersburg. Not the same as St. Pet. Ac. Mm. 
186295. B.M.; Dub.R.I.A. 

. . Nova Acta Academies Scientiarum Imperialis Petropolitame. Petropoli. 
1783-1802. B.M.; Camb.U.; Edinb.R.S.; Linn.S.i.; N.H.M.; 

Oxon.B.; Oxon.R.; P.O.; R.A.S.i.; R.S.; U.C.L. 
.. Recueil des Actes des Seances Publiques de 1'Academie Imperiale 

des Sciences de St. Petersbourg. St. Petersbourg. 
182748. B.M.; Camb.U.; Chem.S.i.; Dub.R.I.A.i.; Edinb.R.S.; 

N.H.M.; Oxon.B.; Oxon.R.i.; R.A.S.; R.S. 
" | See St. Pet. Ac. Sc. Bll. 

j See St. Pet. Ac. Mm. 

. . Memoires presentes a 1'Academie Imperiale des Sciences de St. Peters- 
bourg par divers Savans. St. Petersbourg. 

xliv 



St. Gal. B 

St. Louis AC. T. 



Stockh. Ac. XZndl 

Stockh. Ak. Kndl 

Stockh. Ak. ZZndl. Bh. 



Stockh. Ofv 



Stockfc. Vt. Ak. Lefn. 



St. Pet. Ac. Mm. 



St. Pet. Ac. Sc. Bll 



St. Pet. Ac. Sc. Mm 
St. Pet. Ac. Sc. Mm. ( 



St. Pet. Ac. Sc. N. Acta. 

St. Pet. Ac. Sc. Rcc. .. 



St. Pit. Bll. Ac. Sc 

St. Pet. Bll. Sc 

St. Pet. Mm 

St. Pet. Mm. Ac. Sc 

St. Pet. Mm. Sav. E tr. . 



List of Serial Publications 



Strasb. Mm. S. Sc. 



Strasb. S. Sc. N. Mm. 



Svea 

Sym. Met. IVIg. .. 



Tasm. B. S. P. 



Taylor Sc. Mm 



Tel. E. J. 



Terr. Mag 

Texas Ac. Sc. T 

Thomson A. Ph 



Thrond. Skr 



TillochPh. Mg 



Tok. Coll. Sc. J. 



Tok. Un. Mm. . 



Tor. Ac. Mm. 



Tor. Ac. Sc. At. ... 



Tor. Ac. Sc. Mm. . . . 



183159. B.M.; Camb.U.; Edinb.K.S.; Glasg.U.; Linn.S. ; 

N.H.M.; E.A.S.; B.S.; U.C.L.i. 
Memoires de la Societe des Sciences Naturelles de Strasbourg. 

Strasbourg. 

183070. B.M.; Dub.B.I.A.i.; Dub.T.C.i.; N.H.M. 
Nouveaux Memoires de la Societe des Sciences, Agriculture, et Arts 

du De'partement du Bas-Rhin. Strasbourg. 
183242; 185968. Camb.U.i.; N.H.M.; Oxon.B.; B.S.i. 
Svea. Tijdskrift for Vetenskap och Konst. Upsala. 
181831. 

Symons's Monthly Meteorological Magazine. London. 
1866 Camb.U.; P.O.; B.S. 

Monthly Notices of Papers and Proceedings of the Eoyal Society 

of Tasmania. Hobart. 
1863 B.M.i.; Camb.P.S. i.; Dub.E.D.S.; Edinb.B.S.i.; Linn.S.i.; 

N.H.M.; E.A.S.; E.S. 
Scientific Memoirs, selected from the Transactions of Foreign 

Academies and Learned Societies and from Foreign Journals; 

Taylor. London. 
183752. B.M.; Camb.U.; Chem.S.i.; Edinb.E.S.; Linn.S.i.; 

N.H.M. ; Oxon.B.(B.); P.O.; B.A.S.i.; E.S.; U.C.L. 
Journal of the Society of Telegraph Engineers. London. 
1872 B.M.; Camb.P.S. ; Camb.U. i. ; Dub.T.C.i.; Oxon.B.; 

Oxon.E.; P.O.; E.S.; U.C.L. 

Terrestrial Magnetism [and Atmospheric Electricity]. An Inter- 
national Quarterly Journal. Chicago, Cincinnati, Baltimore. 
1896 Camb.U.i.; E.S. 

Transactions of the Texas Academy of Science. Austin. 
1892 Camb.P.S.; Edinb.E.S.; Glasg.P.S.; Math.S.i.; N.H.M.; 

E.S. 
Annals of Philosophy, or Magazine of Chemistry, Mineralogy, 

Mechanics, and the Arts; Thomson. London. 
181326. B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Edinb.E.S.i.; 

Linn.S.; N.H.M.; Oxon.B.; Oxon.E.; P.O.; E.A.S.; E.S.; 

U.C.L.i. 
Det Kongelige Norske Videnskabersselskabs Skrifter i det 19de 

Aarhundrede. Kjtfbenhavn og Throndhjem. 

1817 B.M.; Camb.U.i.; Dub.T.C.i.; Edinb.E.S.i.; N.H.M.; E.S. 
See Norske Vd. Skr. 

The Philosophical Magazine, comprehending the various branches 

of Science, the Liberal and Fine Arts, Geology, Agriculture, 

Manufactures, and Commerce. London. 
17981826. B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Edinb. 

E.S.i.; Edinb.U.; Glasg.P.S.; Glasg.U.i.; Linn.S.i.; N.H.M.; 

Oxon.B.; Oxon.E.; P.O.; E.A.S.; E.S.; U.C.L. 
The Journal of the College of Science, Imperial University, Japan. 

Tokio, Japan. 
1887 B.M.; Camb.P.S.; Camb.U.; Chem.S.; Dub.T.C.; Edinb. 

E.S. ; Edinb.U.i.; Glasg.P.S.i. ; Linn.S.i.; Math.S.; N.H.M.; 

Oxon.B.; Oxon.E.; P.O.; E.S.; U.C.L. 
Memoirs of the Science Department, University of Tokio, Japan. 

Tokio, Japan. 
187985. Camb.U.; Chem.S.i.; Dub.E.D.S.; Dub.E.I.A.; Edinb. 

E.S.i.; Glasg.P.S.; Linn.S.i.; N.H.M.; Oxon.B.; Oxon.E.; 

B.A.S.i.; E.S.; U.C.L.i. 
Memorie della E. Accademia delle Scienze di Torino. Torino. 

1818 B.M.i.; Camb.P.S.; Camb.U.; Dub.E.I.A.; Edinb.E.S.; 
Glasg.U.i.; Linn.S.; N.H.M.; Oxon.B.; P.O.; E.A.S.; E.S.; 
U.C.L.i. 

See Tor. Ac. Sc. Mm., Tor. Mm. Ac., Turin Ac. Mm. and Turin 

Mm. Ac. 

Atti della E. Accademia delle Scienze di Torino. Torino. 
1865 B.M.; Camb.P.S.; Camb.U.; Chem.S.i.; Dub.E.I.A.; 

Edinb.E.S.; Glasg.U.i.; Linn.S.; N.H.M.; Oxon.B.; P.O.i. ; 

E.A.S.; E.S.; U.C.L.i. 
See Tor. At. Ac. Sc. 
See Tor. Ac. Mm. 



xlv 



d2 



List of Serial Publications 



Tor. At. Ac. Be 

Tor. Lav. Be. Fis. Mt. 



Tor. Mm. Ac 

Tortolinl A 



Toul. Ac. Sc. Bll. . . . 
T oul. Ac. Sc. Mm. . . . 

Toul. Fac. Sc..A. ... 



Tool. Mm. Ac 

TouL Mm. Ac. Sc. . . 

Toul. Obs. A. .. 



Toul. 8. H. Nt. Bll. 

Ts. Mth 

Ts. Mt. Fys 



Turin Ac. Mm. 

Turin Mm. Ac. . . . 



TTn. Serv. I. J 

Ups. Arsk 

Ups. N. Acta S. Sc. 
Ups. 8. Sc. N. Acta 

Tips. Vet. S. Arsk. . . 
V. 8. Coast Sv.Rp... 

Utr. A. Ac 

Utr. Aant. Frv. On. 



Vars. S. Wt. Tr. (C. E. 

Ps. C.) 



Vars. 8. Kt. Tr. (Mm.) 



See Tor. Ac. Sc. At. 

Notizia storica del lavori fatti dalla Classe di Scienze Fisiche e 

Matematiche della E. Accademia delle Scienze negli anni 1864 

65. Torino. 

1869. Linn.S.; E.A.S.; E.S. 
See Tor. Ac. Mm. 

Annali di Scienze, Matematiche, e Fisiche ; Tortolini. Eoma. 
185057. B.M.; Camb.U. i.; Dub.E.D.S.; Dub.T.C.; Edinb.U.; 

Glasg.U.i.; Math.S.i.; Oxon.B.(B.); E.S.; U.C.L. 
See A. Mt. 
Bulletin de 1'Academie des Sciences, Inscriptions et Belles-lettres de 

Toulouse. Toulouse. 

189899. Dub.E.LA.; Edinb.E.S.; N.H.M.; E.S. 
Memoires de 1'Academie des Sciences, Inscriptions et Belles-Lettres 

de Toulouse. Toulouse. 
1782 B.M.; Camb.U.; Dub.E.LA.; Edinb.E.S.i. ; N.H.M.; 

Oxon.B.i.; E.A.S.i.; E.S. 
See Toul. Mm. Ac. and TouL Mm. Ac. Sc. 
Annales de la Faculte des Sciences de Toulouse pour les Sciences 

Math^matiques et les Sciences Physiques. Paris. 
1887 Camb.P.S.; Camb.U.; Edinb.E.S.; Math.S.; Oxon.E.; E.S. 

| See Toul. Ac. Sc. Mm. 

Annales de 1'Observatoire Astronomique, Magnetique et Me'te'orolo- 
gique de Toulouse. Paris. 

1880 B.M.; Edinb.E.S.; Math.S.i.; E.A.S.; E.S. 

Bulletin de la Societe d'Histoire Naturelle de Toulouse. Toulouse. 

1867 N.H.M. 

Tidsskrift for Mathematik. Kjefbenhavn. 

185989. B.M.; Camb.U.; Math.S.i.; Oxon.B. 

Tidskrift for Matematik och Fysik, tillegnad den Svenska Elementar- 
Undervisningen. Upsala. 

186874. B.M.; E.S.i. 

(Memoires de l'Acad6mie Eoyale des Sciences de Turin. Turin. 
<1784 1816. B.M.; Dub.B.I.A.i.; Edinb.E.S.; Linn.S.; Oxon.B.; 
( P.O.; E.A.S.; E.S.; U.C.L. 

See Tor. Ac. 



Journal of the Eoyal United Service Institution. London. 

1858 B.M. ; Camb.U. ; Dub.N.L.I.i. ; Edinb.U. ; Oxon.B.i. ; 

P.O.; E.S. 

Upsala Universitetets Arsskrift. Upsala. 
1861 B.M.; Camb.U.; Dub.E.D.S.i.; Dub.E.I.A.i.; Edinb.E.S.; 

Linn.S.i.; Math.S.i.; N.H.M.; Oxon.B.; E.A.S.i.; E.S. 
| Nova Acta Eegise Societatis Scientiarum Upsaliensis. Upsalise. 
1773 B.M.; Camb.U.; Dub.E.I.A.i.; Edinb.E.S.i.; Glasg.U.i.; 

Linn.S.; Math.S.i.; N.H.M.; Oxon.B.i.; Oxon.E.; E.A.S.i.; 
( E.S.i.; U.C.L.i. 

Arsskrift utgifven af Kongl. Vetenskaps- Societe ten i Upsala. Upsala. 
186061. B.M.; Camb.U.; Edinb.E.S.; N.H.M.; E.S. 
Eeports of the Superintendent of the Coast Survey, showing the 

Progress of the Survey from year to year. Washington. 
1851 Camb.U.; Dub.E.I.A.i.; Edinb.E.S.; N.H.M.; E.A.S.; 

E.S.; U.C.L.i. 

AnnalesAcademiffiBheno-Trajectinse. TrajectiadEhenum. (Utrecht.) 
181537. B.M.; Camb.U.; N.H.M.; Oxon.B.; E.S.i. 
Aanteekeningen van het Verhandelde in de Sectie-Vergaderingen 

van het Provinciaal Utrechtsch Genootschap van Kunsten en 

Wetenschappen. Utrecht. 
1846 Dub.E.D.S.; Edinb.E.S.; E.S. 

Travaux de la Societe des Naturalistes de Varsovie. Comptes 
Eendus de la Section de physique et de chimie. Varsovie. [In 
Eussian.j 

1889 Math.S.; N.H.M. 

Travaux de la Societe des Naturalistes de Varsovie. Memoires. 
Varsovie. [In Eussian.] 

189196. Math.S.; N.H.M. 

xlvi 



List of Serial Publications 



Ven. Aten 

Ven. Aten. At 

Ven. Aten. Esercit. 



Ven. At. X 

Ven. I. At 

Ven. Esercit. Aten. 

Ven. I. Mm 

Ven. Mm. I 



Verona Mm. S. It. . 
Verona S. It. Mm. . 



Viet. R. S. P. .. 



Viet. R. S. T. 



Viet. T. Ph. I. 



Viet. T. R. S. 

V. Nost. Eng. 



Voigt Mg.. 



Wash. Nat. Ac. 
Wash. Ph. 8. Bll. 



W. Eng. J 

Westf. Vr. Jbr. 



Wet. Gs. Jbr. .. 



Wiad. Mt 

WienAk. D 



Atti delle Adunanze dell' I. B. Istituto Veneto di Scienze, Lettere, 

ed Arti. Venezia. 
1841 B.M.; Dub.E.D.S.i.; Dub.B.I.A.i.;Edinb.B.S.i.; Linn.S.i.; 

E.S.i. 

L'Ateneo Veneto: Eivistamensiledi Scienze, Lettere ed Arti. Venezia. 
1881? Dub.B.D.S.i.; E.S.i. 
Atti dell' Ateneo Veneto. Venezia. 
1864 Dub.E.D.S.; E.S.i. 
Esercitazioni Scientifiche e Letterarie dell' Ateneo di Venezia. 

Venezia. 

183760. B.M.i.; Dub.T.C.i.; Oxon. B.i.; E.S.i. 
See Ven. Esercit. Aten. 

f Atti del Eeale Istituto Veneto di Scienze, Lettere ed Arti. Venezia. 
"(1841 B.M.; Edinb.E.S.i.; Linn.S.i.; Math.S.i.; N.H.M.; E.S.i. 

See Ven. Aten. Esercit. 

IMemorie del Eeale Istituto Veneto di Scienze, Lettere, ed Arti. 
I Venezia. 
1843 B.M. ; Camb.U. ; Dub.E.I.A.i. ; Linn.S.i.; N.H.M. ; 

Oxon.B.i.; E.S. 

/Memorie di Matematica e di Fisica della Societa Italiana delle 
1 Scienze. Modena e Verona. 

1 1782 B.M.i.; Camb.P.S.; Camb.U.i.; Dub.E.I.A.; Edinb.E.S.i.; 
( Linn.S.i.; Oxon.B.i.; E.A.S.i.; E.S.; U.C.L.i. 
See Mod. Mm. S. It, and Rm. S. It. Mm. 
Proceedings of the Eoyal Society of Victoria. Melbourne. 
1889 B.M. ; Camb.P.S. ; Camb.U. ; Dub.E.I.A. ; Dub.T.C. 
Edinb.E.S.; Edinb.U.; Glasg.P.S.; N.H.M.; Oxon.B.; Oxon.E. 
P.O.; E.S.; U.C.L.i. 
Transactions and Proceedings of the Eoyal Society of Victoria. 

Melbourne. 

1861 B.M.; Camb.P.S.; Camb.U.; Dub.E.D.S.; Dub.E.I.A.; 
Edinb.E.S.; Edinb.U.; Glasg.P.S.i.; Glasg.U.i.; Linn.S.i.; 
N.H.M.; Oxon.B.; Oxon.B.i.; P.O.; E.A.S.; E.S. 
See Viet. T. R. 8. 
Transactions of the Philosophical Institute (afterwards Eoyal Society) 

of Victoria. Melbourne. 
185560. B.M.; Camb.U.i.; Dub.E.I.A.; Edinb.E.S.; Glasg. 

P.S.i.; Linn.S.; N.H.M.; Oxon.B.; P.O.; E.A.S.; E.S. 
See Viet. R. S. T. 

Van Nostrand's Engineering Magazine. New York. 
186985. B.M.; P.O.; E.S.i. 

. Magazin fur den neuesten Zustand der Naturkunden, mit Eiicksicht 
auf die dazu gehorigen Hiilfswissenschaften ; Voigt. Jena und 
Weimar. 
17971806. B.M.; Camb.U.; N.H.M.; E.S. 

. Memoirs of the National Academy of Sciences. Washington. 

1866 B.M.i.; Camb.P.S.; Camb.U.i.; Dub.E.I.A.; Edinb.E.S.; 

Math.S.i.; N.H.M.; Oxon.B.i.; Oxon.E.; P.O.; E.S.; U.C.L.i. 

Bulletin of the Philosophical Society of Washington. Washington. 

1874 B.M.; Camb.P.S.; Edinb.E.S.; Linn.S.; N.H.M.; Oxon.B.; 

P.O.; E.A.S.; E.S. 
. The West of England Journal of Science and Literature. Bristol. 

183536. B.M.; Camb.U.; Edinb.E.S.; N.H.M.; Oxon.B.; P.O. 
. Jahres-Bericht des Westf alischen Provinzialvereins fur Wissenschaf t 

und Kunst. Miinster. 
1873 N.H.M. 
. Jahresbericht der Wetterauischen Gesellschaft fur die gesammte 

Naturkunde. Hanau. 
1843 Dub.E.I.A.; E.S.i. 
. Wiadomosci Matematyczne. Warsaw. 

1897 Camb.P.S.; Math.S. 
. Denkschriften der Kaiserlichen Akademie der Wissenschaf ten. 

Mathematisch-Naturwissenschaftliche Classe. Wien. 
1850 B.M.; Camb.P.S.i.; Camb.U.; Chem.S.i.; Dub.E.I.A.; 
Edinb.E.S.; Edinb.U.; Linn.S.; N.H.M.; Oxon.B.(E); P.O.i.; 
E.A.S.; E.S.; U.C.L.i. 

See Wien D. 

xlvii 



List of Serial Publications 



Wien Ak. Bb. 



Wien Aim. 



Wien Berg-Hm. Jb. 



Wien D 

Wien Jb. Pol. I. .. 



"Wien Jbr. Ober-Realsch. 
Inn. Btadt 

Wien Met. Z 

Wien Mt. Gg. Gs 

Wien BB ) 

Wien Sb J 

Wise. Ac. T 



Wttrtb. Jh. 



Wurzb. Ps. Did. Sb. 



Wurzb. Ps. Md. Vh. 
Wiirzb. Vh. ... 



Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe 

der Kaiserlichen Akademie der Wissenschaften. Wien. 
1848 B.M.; Camb.P.S.i.; Camb.U.; Chem.S.i.; Dub.R.I.A.; 

Dub.T.C.; Edinb.R.S.i.; Glasg.U.i.; Linn.S.; N.H.M.; Oxon.B.; 

Oxon.B.; P.O.i.; R.A.S.i.; B.S.; U.C.L.i. 
See Wien BB. and Wien Sb. 

Almanach der Kaiserlichen Akademie der Wissenschaften. Wien. 
1851 B.M.; Camb.P.S.i.; Camb.U.; Dub.R.I.A.i.; Edinb.B.S.i.; 

Oxon.B.; P.O.i.; R.A.S.i.; R.S.i.; U.C.L.i. 
Anzeiger der Kaiserlichen Akademie der Wissenschaften: Math.- 

Naturwiss. Classe. Wien. 

1864 Camb.U.; Linn.S.; N.H.M.; Oxon B.; R.S.i. 
Berg- und Huttenmannisches Jahrbuch der k. k. Schemnitzer 

Bergakademie und der k. k. Montan-Lehranstalten zu Leoben 

und Pfibram ; Gustav Faller. Wien. 
1851 B.M.i.; P.O.i. 
See Wien Ak. D. 
Jahrbuch des k. k. Polytechnischen Instituts in Wien; Prechtl. 

Wien. 

181939. B.M.; Camb.U.; Oxon.B.; P.O. 
Jahresbericht der offentlichen Ober-Realschule in der innern Stadt. 

Wien. 
185963. 

Zeitschrif t der Oesterreichischen Gesellschaf t fur Meteorologie . Wien . 
186685. Dub.R.D.S.; Edinb.R.S.; P.O.; R.S. 
Mittheilungen der k. k. Geographischen Gesellschaft. Wien. 
1857 B.M.; Dub.R.I.A.i.; Dub.T.C.i.; N.H.M.; OxonB.; R.S. 

See Wien Ak. Bb. 

Transactions of the Wisconsin Academy of Sciences, Arts and 

Letters. Madison. 
1872 B.M. ; Camb.P.S.; Dub.R.I.A.; Edinb.R.S.; N.H.M.; 

Oxon.R.i.; P.O.i.; R.S. 
Jahreshefte des Vereins fur vaterlandische Naturkunde in Wiirttem- 

berg. Stuttgart. 
1845 B.M.; Camb.U.; Dub.R.D.S. i.; Dub.T.C.i.; Linn.S.i.; 

N.H.M.; R.S. 
Sitzungsberichte der Physikalisch-Medicinischen Gesellschaft zu 

Wiirzburg. Wiirzburg. 
185962. 1881 Camb.P.S.; Camb.U.; Chem.S.i.; Dub.R.I.A.; 

Linn.S.i.; Oxon.R.i.; R.S. 

i Verhandlungen der Physikalisch-Medicinischen Gesellschaft. Wiirz- 
\ burg. 
185060. 1868 B.M.i. ; Camb.P.S. ; Camb.U. ; Chem.S.i. ; 

Dub.R.I.A.; Linn.S.; N.H.M.; Oxon.R.; R.S.; U.C.L.i. 



ZachCor. 

Zach M. Cor 

Z. Bauw :. 

Z. Xnstk 

Z. Mth. Ps. .. 



Z. Ww. 



Correspondance Astronomique, Geographique, Hydrographique, et 

Statistique ; von Zach. Genes. 
181826. B.M.; R.A.S.; R.S. 
Monatliche Correspondenz zur Beforderung der Erd- und Himmels- 

Kunde; von Zach. Gotha. 
180013. Oxon.B.; R.A.S.; R.S.; U.C.L. 
Zeitschrif t fiir Bauwesen; herausg. unter Mitwirkung der konigl. 

technischen Bau-Deputation und des Architecten- Vereins zu 

Berlin. Berlin. 

1851 B.M.; Camb.U.i.; P.O. 
Zeitschrift fiir Instrumentenkunde. Organ fiir Mittheilungen aus 

dem gesammten Gebiete der wissenschaftlichen Technik. Berlin. 
1881 B.M.; Camb.U.; Chem.S.; Edinb.U.; Oxon.R.; P.O.; 

R.A.S.; R.S. 

Zeitschrift fiir Mathematik und Physik; Schlomilch. Leipzig. 
1856 B.M.; Camb.U.; Dub.R.D.S. i.; Dub.R.I.A.i.; Dub.T.C.i.; 

Edinb.U.; Glasg.U.i.; Math.S.i.; Oxon.B.(R.); R.S.; U.C.L.i. 
See Schlomilch Z. 
Zeitschrift fiir die gesammten Naturwissenschaften; herausgegeben 

von dem Naturwissenschaftlichen Vereine fiir Sachsen und 

Thiiringen in Halle; Giebel. Berlin. 

xlviii 



Z. Fsychol 

Zur. Mschr. . 



Ziir.N. D. Scb. Gs.. 



Zwick. Vr. m. Jbr. 



List of Serial Publications 

1853 B.M. ; Camb.U.f. ; Dub.N.L.I.t. ; Dub.B.D.S.t. ; Dub. 

B.I.A.i.; Dub.T.C.i.; Edinb.B.S.; Linn.S.; N.H.M.; Oxon.B.; 

Oxon.E.; B.S. 

See Halle Z. and Halle Z. Nw. 
Zeitschrift fiir Psychologie und Physiologic der Sinnesorgane. 

Hamburg, Leipzig. 

1890 B.M.; Camb.U.; Edinb.U.; Oxon.B.; Oxon.E.; E.S.; U.C.L. 
Monatsschrift des Wissenschaftlichen Vereins in Zurich ; Hitzig, etc. 

Zurich. 

185659. B.M.; Camb.U.; N.H.M.; Oxon.B.; E.S. 
Mittheilungen der Naturforschenden Gesellschaft in Zurich. Zurich. 
184756. Chem.S.i.; Dub.E.I.A.; Edinb.E.S.i.; Linn.S.; N.H.M.; 

E.A.S.; E.S. 
Neue Denkschriften der allgemeinen Schweizerischen Gesellschaft 

fiir die gesammten Naturwissenschaften Neuchatel. Zurich, etc. 
1837 B.M.; Camb.P.S.; Camb.U.; Dub.E.D.S.i; Dub.E.I.A.i.; 

Edinb.E.S.; Linn.S.i.; N.H.M.; Oxon.B.; E.S. 
See Scb. OB. N. 3>. 
Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich. 

Zurich. 
1856 B.M.; Camb.P.S.; Camb.U.t.; Chem.S.i.; Dub.E.I.A.; 

Edinb.E.S.; Linn.S.i.; Math.S.t.; N.H.M.; E.A.S.; E.S. 
Jahresbericht des Vereins fiir Naturkunde zu Zwickau. Zwickau. 
1874 N.H.M.; E.S.i. 



xlix 



PURE MATHEMATICS 

SCHEDULE OF CLASSIFICATION 

ADAPTED FROM SCHEDULE A OF THE INTERNATIONAL 
CATALOGUE OF SCIENTIFIC LITERATURE. 



0000 Philosophy 

0010 History. Biography ... 
History 

Arabian Mathematics 
Greek Mathematics 
Indian Mathematics 
Biography 

0020 Periodicals. Reports of Insti- 
tutions, Societies, Congresses, 
etc 

0030 General Treatises, Text Books, 
Dictionaries, Tables, Collected 
Works 

0032 Bibliographies ... 

0035 Tables of Mathematical Func- 
tions 

0040 Addresses, Lectures, etc., of a 
general character . 

0050 Pedagogy 

0060 Institutions 

0070 Nomenclature ... 

0080 Instruments, including Calcu 

lating Machines. Models 34 

Instruments 34-38 

Calculating Machines 38-39 

Models 39-40 

0090 Aids to Calculation, Graphical 

Processes ... ... ... 40 

ARITHMETIC AND ALGEBRA. 

Foundations of Arithmetic. 
0400 General 42 

0410 Rational numbers ; arithmeti- 
cal operations ... ... 43 

Scales of Notation 45-46 

0420 Existence of irrational and 
transcendental numbers ; in- 
finite processes adapted to 
rational numbers ... ... 46 

0430 Aggregates 49 



PAGE 
1 

3 

. 3-17 
4 
. 9-10 
11 
17-25 
ti- 


0800 
0810 
0820 

0830 
0840 


Universal Algebra. 

General ... 
Calculus of Operations 
General theory of complex 
numbers. (See also 2870.) 
Quaternions 
Ausdehnungslehre ; vector an- 
alysis 


PAGE 

50 
51 

53 

56 

59 


es, 
25 

i 

ed 
25 
... 26 

1C- 


0850 
0860 

0870 
1200 


Matrices 
Other special sorts of complex 
numbers 
Algebra of Logic 

Theory of Groups. 

General . . . 


62 

63 
64 

65 


... 26 
'a 
29 
... 30 
... 32 
33 


1210 
1230 


Discrete groups of finite and 
of infinite order (including 
groups of permutations). 
(See also 2450, 4440.) 
Continuous groups of finite 
and of infinite order 


66 

72 



ALGEBRA AND THEORY OF 

NUMBERS. 
1590 General 75 

Elements of Algebra. 
General ... ... ... ... 75 

Rational polynomials ; divisi- 



1600 
1610 

1615 
1620 



bility ; reducibility 77 

Algebraic inequalities 79 

Permutations, combinations, 
partitions, distributions. 
Binomial and multinomial 

coefficients 80 

Binomial coefficients 80-81 

Chess 81-82 

Combinations ... 82-83 

Magic squares ... 84-85 

Partition of numbers 85-86 



Schedule of Classification 



Partitions 
Permutations 



PAGE 

86-87 
87-88 



Fiqurate numbers ... 89 

Special series 91-92 

Probabilities (including com- 
bination of observations). 
Theory of errors ... 92 
Least Squares Method 97-98 
Probabilities ... 100-103 
Problems ... 101-102 
Theory of statistics. Actu- 
arial mathematics ... 104 
Mortality ... 114-116 
Population ... 117-118 
Calculus of differences; inter- 
polation 121 

Interpolation ... 1 23-1 25 

Linear Substitutions. 

General 126 

Determinants ... ... 127 

Discriminants and resultants 136 
Elimination ... 137-139 

Characteristic properties of 
linear substitutions ; types 
of linear substitutions. 

(See also 1210.) 

General theory of quantics 
Binary forms 
Ternary forms 
Special developments asso- 
ciated with forms in more 
than three variables 



1625 Finite Summation. Recurring 



1630 



1635 



1640 



2000 
2010 
2020 

2030 



2040 
2050 
2060 
2070 



2400 
2410 



2420 
2430 



140 
142 
146 
153 



lf> 5 



2440 



Theory of Equations. 

General 

Elements of the theory of 
algebraicequations; exis- 
tence of roots, symmetric 
functions; rational frac- 
tions ; partial fractions 
Existence of roots 
Symmetric functions 162-163 
Reality, multiplicity, separa- 
tion, of roots 163 

Equations of the second, third 
and fourth orders : other 
particular equations 

Equations, 2nd order ... 
Equations, 2nd, 3rd and 

4th orders 170 

Equations, 3rd order 170-171 
Irreducible case ... 171 

Equations, 3rd and 4th 

orders 171-172 

Equations, 4th order 172-173 
Trinomial Equations 173-174 
Numerical solution of equa- 
tions (including graphical 
methods) 174 



156 



158 
1 59 



169 

169 



PAGE 

Numerical solution of 

equations in general 174 

Approximate determina- 
tion of roots 174-175 
Graphical methods 177-178 
2450 General resolution of equa- 
tions ; theory of Galois. 

(See also 1210.) 178 

Equations, 5th order 180-181 
Equations, 6th order ... 181 
2460 Simultaneous equations ; in- 
cluding linear equations 184 
Linear equations ... 185-186 

2470 Transcendental equations ... 187 

Theory of Numbers. 

2800 General 188 

2810 Divisibility ; linear con- 
gruences ... ... 193 

Divisibility ... 193-194 

2815 Continued fractions and in- 
determinate equations 197 
Continued fractions 197-201 
Indeterminate equations 201-204 
1st order ... 202-203 
2nd order, 3rd order, 4th 

order, 5th order ... 203 

2820 Quadratic residues 204 

2830 Quadratic binary forms ... 205 
2840 Quadratic forms of three or 
more variables ; bilinear 
forms. (See also 2060, 

2070.) 209 

Decomposition of numbers 

into sums of squares 209-2 1 
Bilinear forms ... 21 3-2 1 4 

2850 Congruences other than 
linear ; cubic and higher 

residues 214 

2860 Forms of higher degree which 

cannot be considered as 

products of linear factors. 

(See also 2060, 2070.) ... 218 

Fermafs theorem on 

z n +y n =z n ... 218-219 

2870 Forms of higher degree which 
can be considered as pro- 
ducts of linear factors ; 
algebraic numbers ; ideals. 

(See also 0820.) 220 

2880 Application of trigonometri- 
cal functions to arithmetic ; 

cyclotomy 222 

Binomial equations ... 222 
2890 Application of other trans- 
cendental functions to 

arithmetic 224 

2900 Distribution of prime num- 
bers 225 

2910 Special numbers and numeri- 
cal functions 



Bernoulli's numbers 



228 
228-229 



Schedule of Classification 



2920 Irrationality and transcen- 
dence of particular num- 
bers, such as e and TT. 
(See also 6810.) ... ... 232 

e 232-233 

TT... 233 



3190 General 



ANALYSIS. 



233 



Foundations of Analysis. 

3200 General 234 

3210 Theory of functions of real 

variables 235 

3220 Infinite series ; infinite pro- 
ducts and other infinite 
processes. (See also 5610, 

5620.) 238 

Infinite series ... 238-252 

Binomial theorem 238-239 

Convergence ... 239-241 

Expansion ... 242-244 

Power series ... 245-246 

Summation ... 248-250 

Trigonometric series 250-251 

Infinite products ... 252-253 

Other infinite processes ... 253 

3230 Principles and elements of 

the differential calculus 253 
3240 Taylor's series. Maxima and 
minima ; other analytical 
applications of the differen- 
tial calculus 259 

Lagrange's series ... 261 

Other series 261 

Maxima and Minima 262-263 

Maxima 264 

Minima 264 

Taylor's series ... 265-266 

3250 Principles and elements of 
the integral calculus. Ap- 
proximate integration. 
Mechanical quadrature 267 

Integral calculus 268 

Integration ... 270-272 

3260 Definite integrals (simple) ... 274 

Evaluation ... 277-278 

Transformation ... 280 

3270 Multiple integrals 283 

Double integrals 284-285 

3280 Calculus of variations ... 286 

Theory of Functions of Complex 
Variables. 

3600 General 289 

3610 Uniform functions of one 

variable 292 

3620 Multiform functions of one 
variable ; Rieinann sur- 
faces. (See also 4060, 

6420, 8075.) 296 

Biemann surfaces 296-297 



3630 Expansions in series of func- 
tions, other than powers of 
the variable ... ... 297 

3640 Functions of several variables 298 

Algebraic Functions and their Integrals. 

4000 General 299 

4010 Algebraic functions of one 

variable 301 

4020 Algebraic functions of several 

variables 302 

4030 Logarithmic, circular, ex- 
ponential functions ... 303 
Circular functions 303-305 

Expansion ... 303-304 

Logarithmic and exponen- 
tial functions 305-311 
Logarithmic tables ... 308 
4040 General properties of elliptic 
functions and single theta 
functions ; addition-theo- 
rem. (See also 8050, 8060.) 311 

Addition 311 

Addition-theorem 311-312 
Doubly periodic func- 
tions 312-313 

Elliptic functions... 313-319 

Elliptic integrals 319-321 

Theta functions ... 323-324 

4050 Multiplication,division,trans- 
formation of elliptic func- 
tions; modular functions. 

(See also 4440.) 325 

Division 325 

Modular equations ... 326 
Modular functions . . . 326 

Multiplication ... ... 327 

Transformation ... 327-329 

4060 Abelian integrals. (See also 

8050, 8060.) 329 

A belian functions 329-331 

Abelian integrals . . . 331-333 

Abel's theorem ... 333-334 

4070 Periodic functions of several 
variables ; general theta 
functions 335 

Other Special Functions. 

4400 General 338 

4410 Eulerian functions 339 

Eulerian integrals ... 340 

Gamma functions 340-342 

4420 Legendre's functions; Bessel's 

functions ; hypergeo- 

metric functions ... 342 

Bessel's functions 343-344 

Cylindrical functions ... 344 

Hypergeometric functions 344-345 

Hyper geometric series 345-346 

Legendre's functions 346-347 

Legendre's polynomials 347 

Spherical harmonics 347-348 



liii 



Schedule of Classification 



4430 Polymorphic functions. Other 
functions which may be de- 
fined by definite integrals. 

(See also 4860.) 349 

4440 Automorphic functions. (See 

also 1210, 4050.) 350 

Fuchsian functions 350-351 
4450 Other functions which may 
be defined by linear 
differential equations. 
Lame's functions ... 351 

Lame's functions 352 

4460 Functions which may be de- 
fined by functional equa- 
tions. (See also 6030.) ... 353 

4470 Integral functions 353 

Differential Equations. 
4800 General. (See also 8080 Con- 

nexes.) 354 

4810 Existence theorems for 
ordinary and partial 
differential equations ... 356 

Integrability 356 

4820 Methods of solution and re- 
duction of ordinary differen - 
tial equations ... ... 357 

Equations 358 

Integrals 359 

Integration ... 359-362 

Solution 362-363 

4830 Methods of solution and re- 
duction of partial differen- 
tial equations of first order, 
including the differential 
equations of theoretical 
dynamics ... ... ... 364 

Equations ... ... 364 

Integration ... 365-367 

Solution ... 367-368 

Theory 368 

4840 Methods of solution and re- 
duction of partial differen- 
tial equations of the second 
and higher orders . . . 368 

Equations ... 369-371 

Integrals 371 

Integration ... 371-373 

Solution, ... ... ... 374 

4850 General theory of ordinary 
linear equations. (See also 

4450.) 375 

Equations ... 377-380 

Integrals ... 381-382 

Integration . . . 383-386 

Solution 386-387 

4860 Integration of ordinary linear 
equations by definite inte- 
grals. (See also 4430.) ... 388 
4870 General theory of ordinary 
equations, not linear, of 
the first order 389 



Riccatts equation 390-391 

Solutions ... 391-392 

4880 General theory of ordinary 
equations, not linear, of 
order higher than first ... 392 

Differential Forms and Differential 
Invariants. 

5200 General 393 

5210 Linear differential forms; 

Pfaffians 394 

5220 Differential forms of the 
second and higher orders. 

(See also 8450.) 396 

5230 Transformation of differential 
forms, including tangen- 
tial (or contact) trans- 
formations ... ... 396 

Transformation ... 397-398 

5240 Differential invariants. (See 

also 1230.) 398 

Analytical Methods connected with 
Physical Problems. 

5600 General 400 

5610 Harmonic Analysis ; Fourier's 

series. (See also 3220.) 400 
Fourier's series ... 400-401 

5620 Harmonic Analysis ; series 
other than Fourier's. 
Spherical and ellipsoidal 
harmonics. (See also 3220.) 403 

5630 Generalities on the differen- 
tial equations of mathe- 
matical physics ... ... 404 

5640 Integration of the differential 
equations of mathematical 
physics by series ... ... 406 

5650 Integration of the differential 
equations of mathematical 
physics by definite integrals 407 

5660 Dirichlet's problem and ana- 
logous problems affected by 
boundary conditions ... 407 

Difference Equations and Functional 
Equations. 

6000 General 409 

6020 Solution of equations of finite 

differences 409 

6030 Solution of functional equa- 
tions. (See also 4460.) ... 411 



GEOMETRY. 



6390 General 



412 



Foundations. 

6400 General 412 

6410 Principles of geometry ; non- 
Euclidean geometries ; 
hyperspace ... ... 413 



liv 



Schedule of Classification 



PAGE 

4- Dimensional Space 413-414 
n- Dimensional Space 414415 
Fundamental Principles 415-416 
Non-Euclidean geometry 417-418 
Theory of Parallels 419-420 
6420 Topology of space and hyper- 
space. (See also 3620, 

8075.) 421 

6430 Methods of analytical geo- 
metry. (See also 0840.) 423 
Coordinates ... 425-427 

Elementary Geometry. 

6800 General 429 

6810 Planimetry ; straight lines, 

and circles ... ... 431 

Circles. (See also 2880.) 431-435 
Circle touching 3 given 
circles. (Apollonian 

problem.} 432 

Quadrature of the Circle 434 
Ratio of Diameter to 
Circumference. (See 
also 2920.) ... 434-435 

Polygons. (See also 

7210.) 437-438 

Regular polygons 438-439 

Porisms. (See also 4050 

and 7210.) ... 439-440 

Pythagorean theorem . . . 440 
Quadrilaterals. (See also 

7210.) 

Straight lines 

Triangles (including Cir- 
cles related thereto). 
(For Conic Sections 
related to Triangles 
see 7210.) ... 442^49 

Circles of the Triangle 443-444 
Malfattfs problem ... 444 
Nine-point or Feuerbach 

Circle 444 

Remarkable Points of the 

Triangle ... 446-447 

6820 Stereometry ; straight lines, 
planes, and spheres ; poly- 

hedra 449 

Mensuration of volumes 450-451 

Polyhedra. (See also 8075.) 45 2-456 

Regular Polyhedra ... 454 

Tetrahedra ... 455-456 

Spheres 457-460 

Contacts 458-459 

6830 Trigonometry, plane and 

spherical ... ... ... 461 

Division of Angles and 

Circular Arcs 462-463 

Trisection ... 462-463 

Formulae of Plane Trigo- 
nometry ... 463-465 
Plane Triangles 466-467 
Spherical Trigonometry 468-471 



441 
44^ 



PAGE 

Formulas of Spherical 

Trigonometry 468-469 

Spherical Triangles 470-471 
6840 Descriptive geometry ; ' per- 

spective ......... 472 

Anharmonic or Cross- 

Ratio ...... 472-473 

Axonometry . . . 473-474 

Involution ... ... 475 

Perspective ... 475-476 

Practical Solid Geometry 477 -478 
Protective Geometry 478-480 
Stereographic Projec- 
tions, and other Pro- 
jections of the Sphere. 
(See also 8840 and 
Geography 83.) ... 480 
Trans versals . . . 480-48 1 

Geometry of Conies and Quadrics. 
7200 



481 



7210 



482 
483 



484 
485 



7230 



General ......... 

Equations relating to 

Conies and Quadrics 
Metrical and projective pro- 
perties of conies ... ... 

Conies determined by 

given Points or Tan- 

gents, and Methods of 

Determination . . . 

Contacts ......... 

Curvature of Conies. (See 

also 8430.) ... 485-486 

Ellipses ...... 486-487 

Equations and Coordi- 

nates ...... 487-488 

Foci ...... 488-489 

Hyperbolas ...... 489 

Normals ... 490-491 

Parabola ... 491-492 

Pascal's hexagram, Bri- 
anckon's hexagon, and 
connected figures. (See 
also 807 5.)' ... 492-493 

Polars and Polar Re- 

ciprocals ... 493-494 

Polygons related to 
Conies. (See also 
6810.) ......... 494 

Poncelet's Polygons, Por- 
isms. (See also 4050 
and 6810.) ... 494-495 

Quadrilaterals, Quad- 
rangles, and related 
Conies. (See also 
6810.) ......... 496 

Tangents ... 496-497 

Triangles, and related 
Conies. (See also 
6810.) ...... 497-499 

Systems of conies. (See also 

8070 and 8090.) ...... 499 



Iv 



Schedule of Classification 



PAGE 

Conies with Common 

Focus or Foci ... 500 
7240 Metrical and projective pro- 
perties of quadric surfaces 502 

Axes of Quadric Surf aces 502-503 

Ellipsoid 504 

Equations of Quadrics. 
(See also 2040 and 
7200.) 504-505 > 

Foci and Focal Properties 

of Quadrics ... 505-506 

Generation and Genera- 
tors of Quadrics ... 506 

Hyperboloid and Hyper- 
bolic Paraboloid 506-507 

Inscribed, Circumscribed, 
and Conjugate Figures. 
(See also 7210 and 
8075.) 507-508 

Intersections of Quadrics. 

(See also 7660, 8440.) 508-509 

Normals to Qaadrics ... 510 

Plane Sections of Quad- 
rics 510-511 

Quadrics determined by 
Points, Lines and 
Tangent Planes, and 
Methods of Determina- 
tion 512 

7260 Systems of quadric surfaces. 

(See also 8070, 8090.) ... 513 

Confocal Quadrics ... 513 

Algebraic Curves and Surfaces of degree 
higher than the second. (See also 8070.) 
7600 General 514 

Curves ... ... ... 515 

7610 Metrical and projective pro- 
perties of algebraic plane 
curves of degreehigherthan 
the second. (See also 8030, 

8075,8430.) 517 

Curves, 2nd and 3rd 

degrees ... ... 519 

Curves, 3rd degree 519-522 

Curves, 3rd and 4th, 3rd 

and 5th degrees ... 522 I 
Curves, 4th degree 522-524 

Curvet, 5th, 5th and 6th, 

6th, 14th, mth degrees 524 
Curves, nth degree 524-525 \ 

Curves, nth and pth de- 

rees 525 
plane. algebraic 
^curves. (See also 8030.) 530 

Cartesian ovals ... ... 530 

Curves, 3rd degree 531-532 
Curves, 3rd and 4th de- 
grees 532 

Curves, 4th degree 532-533 

Curves, 5th, 6th degrees 533 



PAGE 

Lemniscates ... 533-534 

7640 Algebraic surfaces of degree 
higher than the second. 

(See also 8040.) 536 

Contacts, and Tangent 
Lines and Planes. (See 
also 8450.) ... 536-537 

Surfaces, 2nd and 3rd, 
2nd, 3rd and 4th, de- 
grees ... ... ... 539 

Surfaces, 3rd degree 539-540 
Configurations. (See also 

8075.) 539 

Surfaces, 3rd and 4th, 
4th, 4th and 5th, 5th, 
(m + n)th, nth degrees 540 
7650 Special algebraic surfaces ... 541 
Anallagmatic surfaces. 

(See also 8020.) ... 541 
Hummer's surface. (See 

also 8060 and 8080.) 542-543 
Steiner's surface ... 544 

Surfaces, 3rd degree, 3rd 

and 4th degrees . . . 545 
Surfaces, 4th degree 545-546 
Surfaces, 5th, 6th, 7th, 
8th, nth, (n + 2)th de- 
grees 546 

Tore or Anchor-ring 546-547 
Wave surface ... ... 547 

7660 Skew algebraic curves. (See 

also 7240, 7660, 8030, 8050. ) 548 
Curves, 3rd degree 548-549 
Curves, 3rd and 4th de- 
grees 549 

Curves, 4th degree 549-550 

Curves, 5th and higher 
degrees ... ... 550 

Transformations and General Methods 
for Algebraic Configurations. 

(References to papers dealing with enumera- 
tive geometry may be found in sections 
8000 to 8100.) 

8000 General 552 

8010 Collineation ; duality ... 552 
8020 Other algebraic transforma- 
tions. (See also 6810, 7650.) 556 
8030 Groups of points on an 
algebraic curve ; genus of 
curves ; principle of corre- 
spondence. (See also 7610, 

7630, 7660.) 560 

Groups of points 562-563 
Involutions ... 563-564 
Principle of correspond- 
ence 564-565 

8040 Groups of curves and points 
on an algebraic surface ; 
genus of surfaces. (See 
also 7640.) 566 



Ivi 



Schedule of Classification 



8050 Application of transcendental 
functions to algebraic 
curves. (See also 4040, 

4060, 7660.) 568 

8060 Application of transcendental 
functions to algebraic sur- 
faces. (See also 4040, 4060, 

7650.) 569 

8070 Enumerative geometry. (See 

also 7230, 7260, 7600-7660.) 570 

8075 Special configurations of 

points, lines, planes or 

other elements. Space 

partitioning. (See also 

3620, 6820, 7210, 7610, 

7640.) 573 

Special configurations of 
points, lines, planes or 
other elements... 573-575 

Space partitioning 575-576 

8080 Line geometry. Connexes, 
complexes, congruences ; 
higher elements of space. 

(See also 7650.) 576 

Line geometry ... 576-577 

Connexes ... ... ... 577 

Complexes 577-580 

Congruences ... 580-582 

Higher elements of space 582 

8090 Systems (linear, and not 
linear) of curves and 
surfaces ... ... ... 582 

Systems of curves. (See 

also 7230.) ... 583-585 

Systems of surfaces 585-586 

8100 Algebraic configurations in 

hyperspace ... ... 586 

^-dimensional space 589 

Infinitesimal Geometry ; applications 
of Differential and Integral Cal- 
culus to Geometry. 

8400 General 589 

8410 Principles of infinitesimal 

geometry ... ... ... 590 

8420 Kinematic geometry. (See 

also Mechanics 0420.) ... 591 
Curve of pursuit ... 591 

Cycloids 592 

Displacement ... 592-593 

Z 'cycloids ... ... 593 
^oocycloids ... ... 594 

Motion 595-596 

Roulettes 597 

8430 Curvature of plane curves ; 
other applications of the 
differential calculus to 
plane curves. (See also 

7210.) 598 

Curves. (See also 7610, 

7630.) 600-602 



PAGE 

Envelopes ... .,. 602 

Evolutes 602-603 

Pedals 604-605 

Radii of curvature 605-606 

Trajectories ... ... 606 

8440 Curvature of skew curves ; 
other applications of the 
differential calculus to skew 
curves. (See also 7240, 8420. ) 607 

Curvature 607 

Curves 607-608 

8450 Curvature of surfaces ; cur- 
vilinear coordinates, and 
other applications of the 
differential calculus to 
surfaces. (See also 5220, 
8810, 8840, 8850.) ... 610 
Curvature of surfaces 610-616 
Indicatrix ... 611-612 

Lines of curvature 612-613 

Measure of curvature 613-614 
Radii of curvature ... 614 
Surface of centres ... 615 

Surfaces 615-616 

Theorems 616 

Curvilinear coordinates 616-618 
Other applications of the 
differential calculus to 
surfaces ... 618-621 

Surfaces 619-621 

8455 Differential geometry of con- 
gruences and other applica- 
tions of the differential cal- 
culus to elements of space 621 
8460 Eectification and quadrature 
of curves ; areas and vol- 
umes of surfaces. Other 
applications of the integral 
calculus to geometry ... 622 

Areas 622-624 

Quadrature . . . 626-62 7 

Rectification ... 627-629 

Volumes ... 629-630 

8470 Special transcendental 

curves. (For cycloids, 
epicycloids and trochoids 

see 8420.) 631 

Spirals 632 

8480 Special transcendental sur- 
faces 632 

8490 Hypergeometric configura- 
tions and higher ele- 
ments of hyperspace ... 633 

Differential Geometry ; applications of 
Differential Equations to Geometry. 

8800 General 634 

8810 Determination of curves on 

surfaces ... ... ... 634 

Curves on surfaces 635-636 

Geodesies 636-638 



Ivii 



Schedule of Classification 



8830 



Geodesies on quadrics. 
(See also Geography 

70.) 

Loxodromes 
Minimal surfaces ... 
Surfaces determined by rela- 
tions of curvature and by 
other differential proper- 
ties 

Surfaces of constant cur- 
vature 

Conformal and other repre- 
sentations of surfaces on 
others. (See also 3600, 
6840 and Geography 70- 
95.) 



PAGE 



638 
639 
640 



642 



643 



645 



8850 



PAGE 

Conformal representation 645-646 



646-647 
647-648 
648 

649-650 
650-651 



Projection 
Representation ... 
Deformation of surfaces 
Deformation 
Surfaces ... 
Orthogonal and isothermic 

surfaces. (See also 5630.) 651 
Isothermic surfaces ... 651 
Orthogonal surfaces 651-653 
8870 Hypergeometric configura- 
tions and higher ele- 
ments of hyperspace ... 653 



APPENDIX 



0000, 0010, 0032, 0035, 0050 ... 654 

0080, 0090, 0400, 0410 655 

0420, 0430, 0830, 0840, 0850, 0870, 

1200, 1210 656 

1230, 1600, 1620, 1625, 1630 ... 657 
1635, 2000, 2010, 2020, 2030, 2040, 

2050, 2060 658 

2070, 2400, 2420, 2430, 2440, 2450, 

2460, 2800, 2810, 2815, 2830 659 
2840, 2850, 2880, 2890, 2900, 2920, 

3200, 3220, 3230, 3240, 3250 660 



3260, 3270, 3280, 3600, 4010, 4040, 

4050, 4060 661 

4420, 4440, 4800, 4830, 4840, 4850, 

4870, 5200, 5210, 5230 ... 662 
5240, 5600, 5610, 5620, 5630, 5660, 
6000, 6400, 6410, 6420, 6430, 

6800, 6810 663 

6820, 6830, 6840 664 

7210, 7230, 7240, 7610, 7630, 7640 665 
7660, 8010, 8020, 8075, 8080, 8090, 

8420, 8430, 8460, 8820 ... 666 



Iviii 



INDEX TO SCIENTIFIC PAPERS FOR 
THE NINETEENTH CENTURY. 

PURE MATHEMATICS. 



0000 Philosophy. 

A posteriori truth. Bing, F. (xn) Ts. Mth. 

3 (1879) 1-. 
. (Bing). Lorenz, L. V. (xn) Ts. 

Mth. 3 (1879) 57-. 
. Bing, F. (xn) Ts. Mth. 3 (1879) 

66-. 
. Lorenz, L. V. (xn) Ts. Mth. 3 

(1879) 118-. 

. Bing, F. (xn) Ts. Mth. 3 (1879) 

122-. 
Aesthetic value of line forms. Wieher, C. 

Karlsruhe Nt. Vr. Vh. 11 (1896) (Ab.) 47-. 
Algebra of relations, principles. Schroder, F. 

[1900] N. Y. Am. Mth. S. Bll. 7 (1901) 

176-. 
Analysis, pure, metaphysics. Piola, G. Bb. 

It. 97 (1840) 315-. 
Aristotle, difference between natural philosophy 

and mathematics according to. Dutordoir, 

. Brux. S. Sc. A. 24 (1900) (Pt. 1), 52-. 
Arithmetization of math'ematics. Pierpont, J. 

N. Y. Am. Mth. S. Bll. 5 (1899) 394-. 
Axioms. Zehender, W. von. Z. Psychol. 19 

(1899) 41-. 
"Begriffsschrift," notation in algebra of logic. 

Frege, G. [1879-82] Jena. Sb. (1879) 29-; 

(1883) 1-. 
of Peano and Frege. Frege, G. Leip. Mth. 

Ps. B. 48 (1896) 361-. 
Choice of forms, importance in mathematics. 

Clariana y Bicart, L. Fschr. Mth. (1891) 

50-. 
Comte's views on philosophy of mathematics. 

Vasiljev, A. V. Kazan S. Ps.-Mth. Bll. 8 

(1899) (Prot.) 11- ; Ens. Mth. 2 (1900) 157-. 
Conception of direction. Dixon, E. T. B. A. 

Ep. (1891) 572. 
space. Hoppe, . D. Nf . Tbl. (*1875) 

142-. 
, an extension of conception of length. 

Graberg, F. Ziir. Vjschr. 31 (1886) 339-. 
, further development. Graberg, F. 

Mr. Vjschr. 32 (1887) 191-. 
Converse of a theorem, truth of; Hauber's 

criterion, applications and generalisations. 

Gunther, S. Arch. Mth. Ps. 56 (1874) 26-. 

VOL. I. 



Correlation of the different branches of ele- 
mentary mathematics. Hayward, R. B. Nt. 

33 (1886) 543-. 
Definition of real number. Burali-Forti, C. 

[1900] N. Y. Am. Mth. S. Bll., 7 (1901) 

158, 170-. 
Definitions. Laurent, H. Ens. Mth. 2 (1900) 

194-. 
. Peano, G. [1900] N. Y. Am. Mth. S. 

Bll. 7 (1901) 158, 168-. 
, theory. Gergonne, J. D. Gergonne A. Mth. 

9 (1818-19) 1-. 
, Whewell's views. Hennessy, J. P. B. A. 

Ep. (1858) (Pt. 2) 3-. 
Demonstration, indirect. De Morgan, A. Ph. 

Mg. 4 (1852) 435-. 
Demonstrations, reduction to simplest form. 

Barre de Saint -Venant, . Par. S. Phlm. 

PV. (1849) 45-. 
Equality, notion of. Burali-Forti, G. Ens. 

Mth. 1 (1899) 246-. 
Equation of the beautiful. Lagout, E. A. Gen. 

Civ. 2 (1863) 141-. 
Ex absurdo proof. Brunei, . Bordeaux S. Sc. 

Mm. 4 (1894) xxxii-. 
Failure of attempt to deduce inductive principles 

from the theory of probabilities. Bryant, S. 

Ph. Mg. 17 (1884) 510-. 

Foundations of the theory of analytical func- 
tions. Timcenko,!. N.Es. S. Nt. Mm. (Mth.} 

12 (1892) 256 pp. ; 16 (1899) 216 pp. ; 19 (1899) 

xv + 183 pp.; Fschr. Mth. (1899) 48-. 
Freedom of the will and physical determinism. 

Hoppe, E. Arch. Mth. Ps. 11 (1892) 339-. 
Function of algebra, chief, formulation and 

simplification of formulae. Ermakow, W. P. 

Fschr. Mth. (1896)47. 
Fundamental operations of arithmetic, the 

five. Kupffer, K. Dorpat Sb. 10 (1895) 359-. 
, order of precedence. Capelli, A, 

Nap. Ed. 39 (1900) 138-. 
principles of human knowledge. Laurent, H . 

Ens. Mth. 1 (1899) 381-. 

General philosophy, aid rendered by mathe- 
matics. Cauchy,A.L. C. E. 21 (1845) 134-. 
Genius in mathematics. Studnicka, F. J. 

Casopis 2 (*1873) 57-; 8 (*1879), 85-; 

Fschr. Mth. (*1873) 54 ; (*1879) 56. 



0000 Philosophy 

Geometric calculus, principles of. Macfarlane, 
A. [1900] N. Y. Am. Mth. S. Bll. 7 (1901) 
158, 178. 

methods considered from the philosophical 
and historical points of view. Galdeano, 
Z. G. de. Fschr. Mth. (1892) 500. 

Geometry applied to practical life. Pearson, K. 
Nt. 43 (1891) 273-. 

as a purely logical system. Fieri, M. [1900] 
N. Y. Am. Mth. S. Bll. 7 (1901) 158, 171-, 
234. 

Hegel and metaphysics of fluxional calculus. 

Smith, W. B. Edinb. K. S. T. 25 (1869) 491-. 
Induction, Aristotle's account. Whewell, W. 

[1850]. Camb. Ph. S. T. 9 (1856) 63-. 

and deduction. Jones, E. E. G. Nt. 46 (1892) 
293-. 

. Russell, F. G. Nt. 46 (1892) 586-. 

. Jones, E. E. G. Nt. 46 (1892) 587-. 

. Dixon, E. T. [1892] Nt. 47 (1892- 

93) 10-. 
. Jones, E. E. C. Nt. 47 (1892-93) 

78-. 
, mathematical. Colecchi, 0. II Progresso, 

17 (1837) 55-. 

, . Wundt, W. Ph. Stud. 1 (*1883) 90-. 
, , applications. Valeriani, V. G. Mt. 15 

(1877) 34-. 

in mathematics. Hadamard, J. [1900] 
N. Y. Am. Mth. S. Bll. 7 (1901) 158, 181. 

Inference, theory of mathematical. Stokes, 

G. J. Am. As. P. (1899) 71. 
Infinite and infinitesimal quantities. Doolittle, 

. Smiths. Misc. Col. 33 (1888) Art. 1, 133-. 

(Wash. Ph. S. Bll. 6 (1884).) 

numbers, various opinions. Cantor, G. 
Stockh. Ak. Hndl. Bh. 11 (1887) No. 19, 
10pp. 

, , Cantor's article. Enestrom, G. 

Stockh. 6'fv. (1885) No. 10, 69-. 

real integers, and their relation to each other. 
Cantor, . D. Nf. [B.] (*1883) 57. 

Infinitesimal calculus, metaphysic of. Sa- 
poretti, A. Bologna Ac. Sc. Mm. 5 (1895-96) 

309-. 
Infinity, conception of in mathematics and 

natural science. Cranz, C. Ph. Stud. 11 

(1895) 1-. 
, mathematical and metaphysical. Frances- 

chinis, F. M. Ven. Aten. Esercit. 1 (1827) 

317-. 
Introduction to course of mathematics. Ger- 

gonne, J. D. Gergonne A. Mth. 21 (1830-31) 

305-. 
Intuition and logic in mathematics. Poincare", 

H. N. Y. Am. Mth. S. Bll. 7 (1901) 71-. 
Iteration as the fundamental mathematical 

operation. Schapira, H. D. Nf. Vh. (1893) 

(Th. 2, Halfte 1), 8-; D. Mth. Vr. Jbr. 3 

(1894) 88-. 

Language, scientific basis of an artificial. Mac- 
farlane, A. N. Y. Mth. S. Bll. 1 (1892) 

189-. 
Law of continuity. An apparent violation. 

Boget, P. M. Ph. Mg. 3 (1828) 118-, 203-. 
Logic and intuition in mathematics and in 

teaching. Poincart, H. Ens. Mth. 1 (1899) 

157-. 



Philosophy 0000 

Logic, mathematical. Peano, G. As. Fr. C. B. 

(1894) (Pt. 2) 222-. 
Logical equalities with three terms. Poretsky, 

P. [1900] N. Y. Am. Mth. S. Bll. 7 (1901) 

158, 172-. 
Mathematical form, theory. Kempe, A. B. 

E. S. P. 38 (1885) 393- ; Phil. Trans. 177 

(1887) 1- ; E. S. P. 42 (1887) 193-. 

problems, and the development of mathe- 
matics. Hilbert, D. Ens. Mth. 2 (1900) 
349-. 

reasoning, nature of. Poincare, H. [1894] 
Kazan S. Ps.-Mth. Bll. 8 (1899) (Prot.) 74-. 

science, relation of parts to fundamental 
idea. Price, B. Ashmol. S. T. 2 (1849) 
23 pp. 

sciences, modern classifications. Dickstein, 
S. Wiad. Mt. 2 (1898) 181- ; Fschr. Mth. 
(1898) 42. 

studies and deductive inference. Pirez, E. 
Mex. S. "Alzate" Mm. 8 (1894) 315-. 

theory of composition of sensations. De La 
Rive, L. Gen. S. Ps. Mm. 30 (1890) No. 4, 
99 pp. 

thought. Newcomb, S. [1893] N. Y. Mth. 
S. Bll. 3 (1894) 95-. 

Mathematics applied to natural history. Bu- 

quoy, G. von. Oken Isis (1825) 1266-. 
, basis of. Lipps, G. F. Ph. Stud. 9 (1894) 

151-, 358-; 10 (1894) 169- ; 11 (1895) 254-; 

14 (1898) 157-. 
, certainty in. Burja, . Berl. Mm. Ac. 

(1802) 3-. 
, experimental groundwork. Hoppe, B. D. 

Nf . Tbl. (*1876) (Beil.) 60-. 
, first notions. Liotard, . Gard Aperpu 

Tr. (1822) 171-. 
, fundamental notions. Cugnin, E. Ev. Sc. 

6 (1896) 193-, 264-. 
, principles. Alexander, S. Silliman 

J. 7 (1849) 178-, 329-. 
, Her hart's view of place in education. 

Greenstreet, W. J. Mth. Gz. No. 2 (1894) 9-. 

and " natural history" <fec., common methods 
of reasoning. Heron, B. Tilloch Ph. Mg. 
11 (1801) 294-. 

and natural science, mutual relations. Wild, 
J. St Gal. B. (1885-86) 101-. 

sciences, relation. Zech, J. D. Nf. 

Vsm. B. (1844) (Ab. 2) 12-. 

and physics, relation to other sciences. 
Jellett, J. H. B. A. Ep. (1874) (Sect.) 1-. 

, study of, influence. Gyory, S. Evk. 2 
(1835) (Pt. 2) 23-. 

and theory of knowledge. Milhaud, G. 
Ev. Sc. 39 (1887) 195-. 

, usefulness to knowledge and mankind. 
Schiibler, E. Oken Isis (1842) 167-. 

Mean values, principle. De Morgan, A. (rx) 
[1853] Camb. Ph. S. P. 1 (1866) 123-. 

Mill's theory of geometrical reasoning mathe- 
matically tested. Smith, W. B. Edinb. E. 
S. P. 6 (1869) 477-. 

Most probable existence, principle of. Gosiewski, 
W. Prace Mt.-Fiz. 3 (1892) 55-; Fschr. 
Mth. (1892) 73-. 

Multiplication and division of concrete quanti- 
ties. Lodge, A. Nt. 38 (1888) 281-. 



0010 History 

Natural laws, mathematical expression. Breton, 

D. [1881] Ev. Sc. 2 (1882) 87-. 

New mathematics, interpretation of old by. 

Halsted, G. B. Texas Ac. Sc. T. 1 (No. 2) 

(1893) 89-. 
Observation in mathematics. Gaillard, G. 

Ev. Sc. 8 (1897) 584-. 
Philosophy of hyperspace. Newcomb, S. [1897] 

N. Y. Am. Mth. S. Bll. 4 (1898) 187-. 
mathematics. Ladame, H. Neuch. Bll. 

2 (1846-47) 213-. 
. Ehrenfels, C. von. Z. Psychol. 

6 (1894) 44, 56-. 

and teaching of mathematics, reduction of 
proofs to simplest form. St Venant,A.J. C.B. 
de. C. B., 83 (1876) 102-, 256-. 

Positive integers, history and philosophy of 
conception. Vasiljev, A. V. Kazan S. Ps.- 
Mth. Bll. 1 (1891) 1- ; Fschr. Mth. (1891) 34. 

psychology and metaphysics, mathematical 
applications. Arnoux, G. As. Fr. C. E. 
(1891) (Pt. 2) 241- ; (1896) (Pt. 2) 45-. 

Principles underlying any deductive theory. 
Padoa, A. [1900] N. Y. Am. Mth. S. Bll. 

7 (1901) 158, 171. 

Probability and its logical significance. Aall, A. 

Arch. Mth. Ntvd. 19 (1897) No. 9, 24 pp. 
Psychological elements of the physico-mathe- 

matical sciences. Smirnov, A. [1895] Kazan 

Un. Mm. 1896 (Pt. 3) 113-, (Pt. 4) 211-, 

(Pt. 5) 147-. 
Pure mathematical sciences, system. Papperitz, 

E. D. Mth. Vr. Jbr. 1 (1892) 36-, 40. 

mathematics, principles. Thiele, T. N. 
(xn) Ts. Mth. 4 (1880) 33-. 

and mixed mathematics, relation. Dyck, W. 
Wiad. Mt. 1 (1897) 139-. 

Bole of mathematics in physics. Bloch-Lyon, 

E. Ev. Sc. 10 (1898) 682-. 
Simplicity, measure of in mathematics. Le- 

moine, E. As. Fr. C. E. (1888) (Pt. 2) 75-. 
Space, philosophic bearing of speculations con- 
cerning realities of. Roberts, S. [1882] L. 

Mth. S. P. 14 (1882-83) 5-. 
in relation to mathematical laws. Raci- 

borski, A. Kosmos (Lw.) 10 (1885) 493-. 
Subject-matter of exact thought. Kempe, A. B. 

[1890] Nt. 43 (1891) 156-. 
Synthetic evolution. Taylor, C. Mess. Mth. 

4 (1868) 181-. 
Theory of numbers, logical investigation. Brix, 

W. Ph. Stud. 5 (1889) 632- ; 6 (1891) 104-, 

261-. 
Time as a fourth dimension (of space). S. 

Nt. 31 (1885) 481. 
Truth, necessary and contingent, in regard to 

principles of science. Powell, B. [1849] 

Ashmol. S. T. 2 (1838-52) 41 pp. 
Zero and infinity. Judson, C. H. Des Moines 

Anal. 8 (1881) 105- ; 9 (1882) 9-. 

0010 History. Biography. 

HISTOEY. 

III. century, value of position for expression of 
numbers known to Eomans in. Vincent, 
A. J. H. C. E. 14 (1842) 43-. 



History 0010 

X. century mathematics, Harib and Garib. 
Steinschneider, M. Z. Mth. Ps. 11 (1866) 235-. 

XII. century mathematics, Abraham Judaeus 
(Savasorda), and Abraham ibn Ezra. Stein- 
schneider, M. [1866]. Z. Mth. Ps. 12 (1867) 
]__ 

, Abraham ibn Ezra. Steinschneider, M. 

Z. Mth. Ps. 25 (1880) (Suppl.) 57-. 
XIV. century arithmetical problems. Curtze, 

M. Bb. Mth. (1895) 77-. 

XIV. and XV. centuries, mathematics. Curtze, 
M. Bb. Mth. (1894) 107- ; (1895) 1-. 

XV. century mathematics, history. Wappler, 
E. Z. Mth. Ps. 45 (1900) (H.-lt. Ab.) 47-. 

XVI. century, arithmetic of Estienne de la 
Eoche. Anon. Ev. Sc. 33 (1884) 561-. 

, books of arithmetic and algebra. Fontes, 

. Toul. Ac. Sc. Bll. 2 (1899) 202-. 

, solution of Euclid's problems with ruler 

and circle of fixed radius, by Italian geo- 
meters. Mackay, J. S. Edinb. Mth. S. P. 
5 (1887) 2-. 

XVII. century, mathematics at beginning of. 
Wolf, R. Bb. Mth. (1889) 33-. 

, mathematics, history. Dickstein, S. 
Bb. Math. (1894) 24. 

, methods of reckoning annuities. 
Enestrom, G. Stockh. Ofv. (1896) 41-; 
Fschr. Mth. (1896) 187. 

XVIII. century, historical development of 
mathematics as an exact science to end of. 
Zeuthen, H. G. Fschr. Mth. (1896) 29. 

mathematics : " II Giornale de' Letterati 

d' Italia" and "La Eaccolta Calogera" as 
sources of history. Loria, G. Z. Mth. 
Ps. 44 (1899) (Suppl.) 241-. 

XIX. century mathematics, historical sketch. 
Clariana y Ricart, L. Barcel. Ac. Mm. 2 
(1892-1900) 539-. 

Abacus, ancient traces. Chasles, M. C. E. 64 

(1867) 1059-. 
, Gerbert's treatise, &c. Chasles, M. C. E. 

16 (1843) 156-, 218-, 281-, 1393- ; 17, 143- . 
, two 12th century treatises. Marducci, E. 

Em. E. Ac. Line. T. 6 (1882) 324-. 
Addition-machines. Unger, F. A. Z. Mth. 

Ps. 44 (1899) (Suppl.) 515-. 
Albert of Saxony : " De proportione dynametri 

quadrati ad costam ejusdem," question of. 

Suter, H. Z. Mth. Ps. 32 (1887) (H.-lt. Ab.) 

41-. 
. Treatise "De quadratura circuli." 

Suter, H. Z. Mth. Ps. 29 (1884) (H.-lt. Ab.) 

81-. 
d'Alembert. Letter to Lagrange. Liouville, J. 

Liouv. J. Mth. 2 (1837) 245-. 
Algebra, early history. Strachey, E. As. Be- 

searches, 12 (1816) 158-. 
, evolution. Hyde, E. W. Am. As. P. 

(1891) 51-. 
, fundamental principles. Macfarlane, A. 

Am. As. P. (1899) 21-. 
, in Germany in 15th century. Curtze, M. 

Z. Mth. Ps. 40 (1895) (Suppl.) 31-. 
, history. Franchini, P. Lucca At. Ac. 3 

(1827) 211-. 
, introduction into Europe, and terminology. 

Chasles, M. C. E. 13 (1841) 497-, 601-. 

3 A2 



0010 History 

Algebra, introduction into Europe, and ter- 
minology. Libri, G. C. B. 13 (1841) 559-. 

in Italy since Fibonacci. Gerhardt, C. I. 
Grunert Arch. 3 (1843) 284-. 

, various names for. Nesselmann, G. H. F. 

N. A. Mth. 14 (1855) 445-. 
Algebraic notation, history. Starkov, A. P. 

Kazan S. Nt. (Ps.-Mth.) P. 3 (1885) 107-. 
Algebraical functions, development of theory 

down to present time. Brill, A., & Noether, 

M. D. Mth. Vr. Jbr. 3 (1894) 107-. 
Algorithm, Bolyai's. Farkas, G. Mag. Tud. 

Ak. Etk. (Mth.) 8 (1881) No. 3, 8 pp. 

of Christan of Prachatic. Studnicka, F. J. 
Prag Sb. (1892) (Mth. Nt.) 100- ; (1893) 
(Mth. Nt.), No. 6, 14 pp. 

, Sacrobosco's, nine "limits" in. Enestrom, 

G. Bb. Mth. (1897) 97-. 
Algorithms, ancient. Jacobi, C. G. J. Berl. 

B. (1850) 426-. 
, work on, 12th century, and on the spread 

of Indo-Arabic arithmetic and ciphers in 

the West. Nagl, A. Z. Mth. Ps. 34 

(H.-lt. Ab.) 129-, 161-. 
, writing on, 12th century. Curtze, M. Z. 

Mth. Ps. 42 (1897) (Svppl.) 1-. 
Algorithmus linealis of H. Stromer (1512). 

Gunther, S. [1880] Prag Ab. 10 (1881) 

(Mth.) No. 4, 18 pp. 
Alhazen's problem. Baker, M. Am. J. Mth. 

4 (1881) 327-. 
Alternants, history. Muir, T. Edinb. B. S. 

P. 23 (1902) 93-. 
America (U.S.), study of mathematics. Cajori, 

E. Bb. Mth. (1891) 74-. 
Analytical geometry, discovery, and work of 

Ghetaldi, 1630. Gelcich, E. Z. Mth. Ps. 27 

(1882) (Suppl.) 191-. 
Ancient problems, two. Saalschutz,L. Konigsb. 

Schr. 39 (1898) [8]-. 
Ancients, numerals of. Saalschiitz, L. Konigsb. 

Schr. 33 (1892) [4]-. 
Angle-measurements by means of Hipparchus' 

dioptra. Hultsch, F. Z. Mth. Ps. 44 (1899) 

(Suppl.) 191-. 
Apparatus for calculation, arithmetical puzzles. 

Lucas, E. Bv. Sc. 45 (1890) 1-. 
Approximation methods, ancient. Gunther, S. 

D. Nf. [B.] (* 1877) 95-. 

, , in light of modern mathematics. 
Gunther, S. Prag Ab. 9 (1878) (Mth.), No. 4, 
44pp. 

Arabian Mathematics. 

Ahmed ibn Yusuf. Liber de similibus arcubus. 
Curtze, M. Bb. Mth. (1889) 15-. 

Ahmed and his book on proportion . Cantor, M. 
Bb. Mth. (1888) 7-. 

Algebraic geometry of Musa al-Kharizmi. 
Marre, A. N. A. Mth. 5 (1846) 557-. 

Arabian algebra, MS. of Al-Khayyami with geo- 
metric construction for cubic equations 
Woepcke, F. Crelle J. 40 (1850) 160-. 

. "Messahat" of Musa al-Kharizmi. 

Marre, A. A. Mt. 7 (1865) 269-. 

algebraic notations. Woepcke, F. C E 39 
(1854) 162-. 



Arabian Mathematics. 



History 0010 



Arabian Mathematics, continued 
Arabian arithmetic, history. Vaux, C. de. 
Bb. Mth. (1899) 33-. 

astronomers and mathematicians. Suter, H. 
Bb. Mth. (1897) 83-; (1899) 86-. 

astronomy and arithmetic. MS. in pos- 
session of Chasles. Marre, A. Bm. At. 
N. Line. 19 (1866) 362-. 

books of the viceregal library in Cairo, 5th 
vol. of catalogue. Suter, H. Z. Mth. Ps. 38 
(1893) (H.-lt. Ab.) 1-, 41-, 161-. 

calculation . ' ' Talkhis ' ' of Ibn al-Bannah . 
Marre, A. Bm. At. N. Line. 17 (1864) 289-. 

MSS., historical extracts. Woepcke, F. C. 
B. 31 (1850) 715-. 

, two, in Berlin Boyal Library. Suter, H. 

Bb. Mth. (1898) 73-. 

methods for finding sin 1 approximately. 
Woepcke, F. Liouv. J. Mth. 19 (1854) 153- , 
302-. 

numerals. Cantor, M. (vi. Adds.) Heidi. 
Vh. Nt. Md. 3 (1862-63) 5-. 

Arabic numerals, geom. form. Dubois-Maison- 

neuve, . Par. Tr. S. Amat. 2 (1808) 51-. 
Arabs, binomial theorem, as known to. Tytler, 

J. As. Besearches 13 (1820) 457-. 
, books of. Steinschneider, M. Z. Mth. Ps. 

10 (1865) 456-. 
, geometrical construction of equations of 4th 

order. Woepcke, F. Liouv. J. Mth. 8 (1863) 

57. 
, progressions among. Gunther, S. Z. Mth. 

Ps. 21 (1876) (Svppl.) 57-. 

and root extraction. Tytler, J. As. Be- 
searches 17 (1832) 51-. 

Biography of Ibn al-Bannah (13th cent.). 

Marre, A. Bm. At. N. Line. 19 (1866) 1-. 
Diophantus among Arabs of 9th century. 

Steinschneider, M. Z. Mth. Ps. 10 (1865) 499. 
Euclid, bibliographical study. Steinschneider, 

M. Z. Mth. Ps. 31 (1886) (H.-lt. Ab.) 81-. 
Hero's square-root formula in Arabian mathe- 
matics and in Begiomontanus's writings. 

Curtze, M. Z. Mth. Ps. 42 (1897) (H.-lt. 

Ab.) 145-. 
Historical notes. Chasles, M. C. B. 40 (1855) 

782- ; 60 (1865) 601-. 
Ibn-al-Haitam, quadrature of the circle. Suter, 

H. Z. Mth. Ps. 44 (1899) (H.-lt. Ab.) 33-. 
Indian numerals, employment by Arabs. 

Woepcke, F. Tortolini A. 6 (1855) 321-. 
Yusuf ibn Ibrahim and Ahmed ibn Yusuf. 

Steinschneider, M. Bb. Mth. (1888) 49-, 

111-. 
Khelasat al Hisab. Marre, A. N. A. Mth. 5 

(1846) 263-. 
Multiplication and division. Latin abridgement 

of an Arabian work on numbers, written by 

N. O'Creat to Adelhard of Bath in 12th 

century (fragment). Henry, C. Z. Mth. Ps. 

25 (1880) (Suppl.) 129-. 
Musa ibn Shakir, sons of, 10th century. 

Steinschneider, M. Bb. Mth. (1887) 44-, 

71-. 
Badical axis probably discovered by Arabs. 

Merrifield, C. W. L. Mth. S. P. 2 (1869) 

175-. 



0010 History 

Arbogast's rule, history of. Tanner, H. W. L. 

Mess. Mth. 20 (1891) 83-. 
Arithmetic book, oldest German, linger, F. 

Z. Mth. Ps. 33 (1888) (H.-lt. Ab.) 125-. 
, historical. Ferrari, G. Mil. I. Lomb. Ed. 

8 (1875) 5-, 227-, 289-, 624-, 1006- ; 9 (1876) 

199-. 
, primitive. Tylor, E. B. Midi. Ntlist. 15 

(1892) 192. 

teaching, beginnings of, in middle ages. 
Cantor, M. D. Nf. Tbl. (1889) 190. 

, treatise (1478). Boncompagni, B. Em. At. 

16 (1862-63) 1-, 101-, 300-, 389-, 503-. 
Arithmetical questions, primitive solutions. 

Bobynin, V. V. Bb. Mth. (1894) 55-. 

triangle, history. Fontes, . As. Fr. C. 
E. (1893) (Pt. 2) 236-. 

and other notes from mediaeval mathe- 
matics. Steinschneider, M. Bb. Mth. (1889) 
35-. 

Assurance, history. Farren, E. J. Assur. Mg. 
[1 (*1851)] 40-. 

. Hendriks, F. Assur. Mg. 2 (*1852) 

121-, 222-; 3 (1853) 93-. 

, first Parliamentary Committee. Hend- 
riks, F. Assur. Mg. 4 (*1854) 58-, 119-, 
300-. 

Babylonian mathematics. Cantor, M. D. Nf. 
Tbl. (*1879) 75-. 

Barrett, G., and F. Baily, correspondence be- 
tween. De Morgan, A. Assur. Mg. 4 (* 1854) 
1 8r5 . 

Barrow, Isaac. Zeuthen, H. G. Kjtfb. Ov. 
(1897) 565-. 

Barycentric calculus of Mobius. Allardice, R. 
E. Edinb. Mth. S. P. 10 (1892) 2-. 

Bernoulli, Daniel, life and works. Basel Vh. 
7 (1885) (Anhang) 3-. 

, John 1st, three letters to Euler in library 
of Stockholm Academy. Enestrom, G. 
[1879] Stockh. Ak. Hndl. Bh. 5 (1880) 
No. 21, 24 pp. 

Besson, Jacques (t!569), work of. (Mathe- 
matical instruments.) Beck, T. Civing. 36 

(1890) 191-. 

Betti, Brioschi, and Casorati, comparison of 

work of. Volterra, V. [1900] N. Y. Am. 

Mth. S. Bll. 7 (1901) 60-. 
Binomial theorem, demonstration (Pascal). 

Delegue, . Dunkerque Mm. S. Encour. 

14 (1869) 163- . 
, historical paradox. Bourgoin, L. Ev. 

Sc. 7 (1874) 453-. 
before Newton. Marre, A. N. A. Mth. 

5 (1846) 488-. 
Boetius, MS. of Alexandrine Library containing 

apices of, without abacus and with values of 

position. Narducci, E. Em. E. Ac. Line. 

Mm. 1 (1877) 503-. 
, notes on. Steinschneider, M. Bb. Mth. 

(1891) 113. 

, pseudo-geometry. Tannery, P. Bb. Mth. 

1 (1900) 39-. 
question. Weissenborn, H. Z. Mth. Ps. 24 

(1879) (Suppl.) 167-, 185-. 
Bohemian mathematicians, some. Teige, K. 

Casopis 22 (1893) 244- ; Fschr. Mth. (1893- 

94) 15. 



History 0010 

Bologna University, mathematical faculty. 

Gherardi, S. [1844]. Bologna N. Cm. 8 

(1846) 519-. 
, , historical notes. Gherardi, S. 

Arch. Mth. Ps. 52 (1871) 65-. 
Bolyai, Janos, investigations in non-Euclidean 

geometry. Stdckel, P. Mth. Termt. Ets. 

18 (1900) 241- ; Mth. Nt. B. Ung. 17 (1901) 

, , letter, 1823, theory of parallels. Szily, 

K. Mth. Termt. Ets. 5 (1887) 187- ; Mth. 

Nt. B. Ung. 5 (1886-87) 189-. 
_, _, work. Schmidt, F. D. Mth. Vr. Jbr. 4 

(1897) 107-. 
Bolyai's theory of imaginaries. Stackel, P. 

Mth. Termt. Ets. 17 (1899) 259-; Mth. Nt. 

B. Ung. 16 (1899) 263-. 
Boncompagni, Baldassarre, history of physics 

and mathematics. Favaro, A. Ven. I. At. 

4 (1894-95) 509-. 
Boskovic, Eoger Josef. Seydler, A. Casopis 

16 (1887) 267-. 
Brachistochrone problem, an historical essay. 

Compere, C. Liege S. Sc. Mm. 1 (1899) 

No. 2, 128 pp. 
Byzantine analecta. Heiberg, J. L. Z. Mth. 

Ps. 44 (1899) (Suppl.) 161-. 

mathematics. Heiberg, J. L. Kjtfb. Ov. 
(1887) 88-; Z. Mth. Ps. 33 (1888) (H.-lt. 
Ab.) 161-. 

Calculating genius. Colburn, Zerah (American 

boy). Saint, W. Nicholson J. 34 (1813) 

291-. 
. , , methods. Ellis, S. Nicholson 

J. 35 (1813) 9-. 
, Inaudi. Flammarion, C. As. 11 (1892) 

114-. 

, Touraine herd-boy's calculating feats. 
Cauchy, A. L. C. E. 11 (1840) 952-. 

machines, history. Mehmke, R. D. Mth. 
Vr. Jbr. 3 (1894) 59-. 

Calculation in columns before 10th century. 
Friedlein, G. Z. Mth. Ps. 9 (1864) 297-. 

, evolution. Friedlein, G. Z. Mth. 

Ps. 10 (1865) 241-. 

, "Gobari" method, 14th century MS. in 
Vatican on method borrowed from. Nar- 
ducci, E. Bll. Sc. Mth. As. 7 (1883) 247-. 

in 16th century. Treutlein, P. Z. Mth. 
Ps. 22 (1877) (Suppl.) 1-. 

Calculus, infinitesimal, invention. Bertrand, 
J. J. Sav. (1862) 465-. 

of probabilities, historical notes. Gabba, A. 
Brescia Cm. (1840) 203-. 

, . Cantor, G. Halle Nf. Gs. B. 

(1873) 34-. 
, origin and progress. Brown, S. 

Assur. Mg. 6 (*1857) 134-. 
" Victorii" (Victorius of Aquitaine in 5th 

century). Tables of weights and measures, 

squares of numbers &c. Kinkelin, H. [1868] 

Basel Vh. 5 (1873) 147-. 

of Victorius. Friedlein, G. Z. Mth. Ps. 
16 (1871) 42-, 253-. 

Cambridge Phil. Soc., history. Clark, J. W. 

Camb. Ph. S. P. 7 (1892) i-. 
Cantor's history: 13th century solution of a 

cubic. Zeuthen, H. G. Kjrfb. Ov. (1893) 1-. 



0010 History 



Cantor's history: 13th century solution of a 
cubic, comment on. Gram, J. P. Kjjefb. 
Ov. (1893) 18-. 

mathematical works, memoirs and critiques. 
Curtze, M. Z. Mth. Ps. 44 (1899) (Suppl.) 
625-. 

Caporali, Ettore, scientific work. Loria, G. 

G. Mt. 27 (1889) 1-. 
Cardan's formula, historic note. Forestier, C. 

Toul. Ac. Sc. Mm. 6 (1874) 254-. 
Cardanus, Hieronymus (1501-1576), work of. 

Beck, T. Giving. 35 (1889) 511-. 
Carnot, Lazare. Arago, D. F. J. Par. Mm. 

de PL 22 (1850) (H.) 1-. 
Casanova de Seingalt. Henry, C. Ev. Sc. 33 

(1884) 503-. 
Case book of John Eowe, London and Exeter, 

1775 to 1790. Hendriks, F. Assur. Mg. 7 

(*1858) 136-. 
Cataldi, inventor of continued fractions. 

Grunert, J. A. Grunert Arch. 30 (1858) 

275-. 
Cauchy as founder of theory of determinants. 

Studnicka, F. J. [1876] Prag Ab. 8 (1877) 

(Mth.) No. 3, 39 pp. 
Cauchy's "Lecons sur le Calcul Diffe'rentiel " 

criticism. Matzka, W. Grunert Arch. 4 

(1844) 357-. 

works. David, . Toul. Ac. Sc. Mm. 4 
. (1882) 178-. 

Cebysev's (Tchebisheff) works on the theory of 

linkages. Delaunay, N. Z. Mth. Ps. 44 (1899) 

(H.-lt. Ab.) 101 -. 
Chasles, Michel, scientific work. Ligin, V. 

N. Es. S. Nt. Mm. (Mth.) 3 (*1881). 
Chinese mathematics. Bertrand, J. J. Sav. 

(1869) 317-, 464-. 
-- , algebra. Matthiessen, H. F. L. Z. Mth. 

Ps. 19 (1874) 270-. 
-- , arithmetic. Biernatzki, K. L. Crelle J. 

52 (1856) 59-. 
-- , and algebra. Biernatzki, K. L. N. 

A. Mth. 2 (1863) 529-. 
-- , problem of Sun-tsze and Yih-hing on re- 

mainders. Matthiessen, H. F. L. [1880-81] 

Crelle J. Mth. 91 (1881) 254-; Z. Mth. Ps. 

26 (1881) (H.-lt. Ab.) 33-. 
Circle, quadrature, A.D. 1580-1630. Glaisher, 

J. W. L. (vn) [1873] Mess. Mth. 3 (1874) 

, (historical). Schubert, H. Smiths. Ep. 
(1890) 97-. 

, -- . Fricke, R. Braunschw. Vr. Nt. 
Jbr. 11 (1899) 184. 

, . S. van der Eycke. Bierens de Haan, 
D. N. Arch. Wisk. 1 (*1875) 70-, 206-. 

Clairaut, Alessio Claudio, letters. Boncom- 

pagni, B. Em. N. Line. At. 45 (1892) 

157-. 
Codex (Liber Algorizmi) in Salem monastery. 

Cantor, M. Z. Mth. Ps. 10 (1865) 1-. ' 
Complex quantities, history. Brunei, W. Bor- 

deaux S. Sc. Mm. 5 (1890) Ixxvi-. 
Condorcet, Marie Jean Antoine Nicolas Caritat, 

Marquis de. Arago, D. F. J. Par. Mm de 

I'l. 20 (1849) (H.) 1-. 

. ------ , -- . 1743-94. EoUnet, 

. Ev. Sc. 52 (1893) 554-. 



History 0010 

Conic section compass, the first. Braunmiihl, 
A. von. Z. Mth. Ps. 35 (1890) (H.-lt. Ab.) 
161-. 

sections (historical account). Zeuthen, H. 
G. Kjrfb. Dn. Vd. Selsk. Skr. 3 (1885-86) 1-. 

Continuity, historical note on. Taylor, (Rev.) 

C. B. A. Ep. (1884) 645-. 
Coordinate geometry in antiquity. Zeuthen, 

H. G. Kjrfb. Ov. (1888) 127-. 
Copernicus, biographical sketch. Studnicka, 

F. J. Casopis 2 (*1873) 1-. 
Cotes, Eoger, historical note. Terquem, 0. 

N. A. Mth. 9 (1850) 195-. 
Counting with fingers <fec., ancient methods. 

Marre, A. A. Mt. 6 (1864) 93-. 
Cube, duplication, ancient methods for. 

Mackay, J. S. [1885]. Edinb. Mth. S. P. 

4 (1886) 2-. 
, , and Delphic oracle. Schweigger, J. S. C. 

Grunert Arch. 9 (1847) 115-. 
Curves and surfaces, history. Tannery, P. 

Bll. Sc. Mth. As. 7 (1883) (Pt. 1) 278-. 
Cusa, Nikolas de, in connection with mathe- 
matical and physical geography. Gilnther, 

S. Z. Mth. Ps. 44 (1899) (Suppl.) 123-. 
Cyphers, holocryptic. Chase, P. E. Camb. 

(U. S.) Mth. M. 1 (1859) 194-. 
Dalton's early writings. Wilkinson, T. T. 

Manch. Ph. S. Mm. 12 (1855) 1-. 
Decimal fractions, history of. Hunrath, K. 

Z. Mth. Ps. 38 (1893) (H.-lt. Ab.) 25-. 
, invention of. Grosse, . Brem. Ab. 14 

(1898) 168-. 

numeration among the ancients. Chasles, 
M. C. E. 6 (1838) 678-; 8 (1839) 72-; 9 
(1839) 447-, 463-. 

point, introduction in arithmetic. Glaisher, 
J. W. L. B. A. Ep. 43 (1873) (Sect.) 
13-. 

Decline of mathematical study and sciences. 
Toplis, J. Tilloch Ph. Mg. 20 (1805) 25-. 

Decomposition of fraction into quantiemes 
(fractions with unity for numerator). Boby- 
nin, V. V. Z. Mth. Ps. 44 (1899) (Suppl.) 

Definite integrals, historical note. Escher, R. 

J. N. Arch. Wisk. 18 (1891) 142-. 
"De inquisicione capacitatis figurarum," 

anonymous work of the 15th century. 

Curtze, M. Z. Mth. Ps. 42 (1897) (Suppl.) 

29-. 
Desargues, works. Chasles, M. C. E. 20 (1845) 

1550-. 

and Pascal on conic sections. Gerhardt, C. 
I. Berl. Ak. Sb. (1892) 183-. 

Descartes. "Calcul de Mons. Des Cartes ou 
Introduction a sa Geometric, 1638." Adam, 
H. Bll. Sc. Mth. 20 (1896) 221-. 

. "Excerpta ex MSS. E. Des-Cartes." 
Tannery, P. Z. Mth. Ps. 44 (1899) (Suppl.) 
501-. 

and Huygens : unpublished letters. Bierens 
de Haan, D. Z. Mth. Ps. 32 (1887) (H.-lt. 
Ab.) 161-. 

and MSS. of Snellius. Korteweg, D. J. N. 
Arch. Wisk. 3 (1898) 57-. 

, a neglected memoir of. Jonquieres, de. 
C. E. 110 (1890) 261-. 



0010 History 

Descartes, philosophical method. Jacobi, C. 

G. J. [1846] Liouv. J. Mth. 12 (1847) 97-. 
, posthumous work on polyhedra. Jonquieres, 

de. C. E. 110 (1890) 315- . 
, services to the exact sciences. Studnicka, 

F. J. Casopis 26 (1897) 73-; Fschr. Mth. 

(1897) 7-. 
, work hitherto unpublished: " De Soli- 

dorum Elementis." Jonquieres, de. Bb. 

Mth. (1890) 43-; Par. Ac. Sc. Mm. 45 (1899) 

325-. 
Descriptive geometry, Monge's (Ikonognosie). 

Tiller, F. Prag Ab. 9 (1878) (Mth.) No. 3, 

88pp. 
Determinants, history and theory. Gunther, 

. D. Nf. Tbl. (*1874) 78-. 
, an overlooked discoverer in the theory. 

Muir, T. Ph. Mg. 18 (1884) 416-. 
, skew, history. Muir, T. [1900] Edinb. 

E. S. P. 23 (1902) 181-. 

, theory, in the historical order of its de- 
velopment. Muir, T. Edinb. E. S. P. 13 
(1886) 547-; 14 (1888) 452-; 15 (1889) 481- ; 
16 (1890) 207-, 389-, 748-. 

, , origin and development. Studnicka, 

F. J. Casopis 5 (*1876) 1-, 88-, 193-, 279-. 
Differential calculus. Enestrom, G. [1878] 

Ups. Arsk. (1879) 71 pp. 

. Enestrom, G. Stockh. Ofv. (1894) 
297-; Fschr. Mth. (1893-94) 66-. 

, history and philosophy. Simon, M. Z. 

Mth. Ps. 42 (1897) (Suppl.) 113-. 
, inventor, &c. Gerhardt, C. I. Grunert 

Arch. 27 (1856) 125-. 
, supposed discovery by Indian astronomer. 

Spottiswoode, W. As. S. J. 17 (1860) 221-. 
, work of Taylor and Nicole. Enestrom, 

G. Stockh. Ofv. (1894) 177- ; Fschr. Mth. 
(1893-94) 65. 

and integral calculus, history. Studnicka, 
F. J. Casopis 8 (*1879) 1-, 97-, 272-; 
Fschr. Mth. (1879) 39. 

, and philosophy. Simon, M. 
D. Nf. Vh. (1896) (Th. 2, Halfte 1) 257-. 

, origin and progress. Gabba, A. 

Brescia Cm. (1825) 89-. 
Digits introduced in Europe. Cantor, M. 

Schlomilch Z. 1 (1856) 65-; 3 (1858) 325-. 

and numeration, history. Friedlein, G. Z. 
Mth. Ps. 9 (1864) 73-. 

, origin. . Sedillot, L. A. Em. At. N. Line. 
18 (1865) 316-. 

, , and the abacus. Vincent, A. J. H. 
Liouv. J. Mth. 4 (1839) 261-. . 

, , (Vincent's paper). Ger son- 
Levy, . Metz Mm. Ac. 21 (1839-40) 336-. 

,origination. Gerhardt, C. I. Grunert Arch. 
2 (1842) 427-. 

Directions of modern mathematical investiga- 
tions. Zorawski, K. Wiad. Mt. 3 (1899) 
48-; Fschr. Mth. (1899) 69. 

Dirichlet and Kronecker, correspondence. 
Gott. Nr. (1885) 361-. 

Division in extreme and mean ratio, historic 
note on expression. Terquem, 0. Liouv. J. 
Mth. 3 (1838) 97-. 



History 0010 

Dominicus Parisiensis. Curtze, M. Bb. Mth. 

(1895) 107-. 

Double periodicity, Jacobi's share in discovery. 

Gundelftnger, S. Bert. Ak. Sb. (1898) 342-. 
Dresden, Eoyal Public Library, MS. in. Curtze, 

M. Z. Mth. Ps. 28 (1883) (H.-lt. Ab.) 1-. 
Egypt, arithmetic in ancient. Loria, G. Bb. 

Mth. (1892) 97-. 
Egypt, mathematics and astronomy in ancient. 

Isely, L. Neuch. S. Sc. Bll. 23 (1895) 23-. 
Egyptian arithmetic. Berg, F. J. van den. N. 

Arch. Wisk. 19 (1892) 211-. 

geometry, history of ancient. Weyr, E. 
Wien Aim. 34 (1884) 213-. 

papyrus, calculator's manual. Rodet, L. 
Par. S. Mth. Bll. 6 (1878) 139-. 

" Encyklopadie der mathematischen Wissen- 

schaften." Meyer, W. F. Z. Mth. Ps. 44 

(1899) (Suppl.) 293-. 
Epitaphs of mathematicians. Isely, L. Neuch. 

S. Sc. Bll. 27 (1899) 167-. 
Equation problem of A. Eomain solved by 

Vieta, letter of Fermat. Ritter, F. Bll. 

Sc. Mth. As. 4 (1880) (Pt. 1) 171-. 
Equations of 3rd order, general solution, 

historical note. Verdam, G. J. Amst. I. 

(1846) 163-. 
Errors, mathematical. Epstein, S. S. Bern 

Mt. (1893) 183-. 
Euler, extract referring to memoir of. Liou- 

ville, J. Liouv. J. Mth. 19 (1874) 189-. 
and his works. Bertrand, J. J. Sav. 

(1868) 133-. 
Euler's constant, history. Glaisher, J. W. L. 

[1871] Mess. Mth. 1 (1872) 25-; 2 (1873) 64. 

correspondence with Pontoppidan. Hansted, 
B. Bll. Sc. Mth. As. 3 (1879) 26-. 

letters to Jean Bernoulli. Enestrom, G. 
Bb. Mth. (1897) 51-. 

use of i. Beman, W. W. N. Y. Am. Mth. 
S. Bll. 4 (1898) 274, 551. 

works, new list. Hagen, J. G. D. Nf. Vh. 

(1896) (Th. 2, Halfte 1) 43-. 

Exact sciences, history of, and the need of 
study. Rosenberger, F. Z. Mth. Ps. 44 

; (Suppl.) 359-. 
Exponents, Cartesian notation. Vincent, A. 

J. H. N. A. Mth. 6 (1847) 35-. 
Fergola, Nicola, and his school of mathematics. 

Loria, G. Genova Un. At. [11] (1892) 363-. 
Fermat, date of principal discoveries. Tannery, 

P. Bll. Sc. Mth. As. 7 (1883) (Pt. 1) 116-. 
, a demonstration by. Wertheim, G. Z. 

Mth. Ps. 44 (1899) (H.-lt. Ab.) 4-. 
, MS. by. Genocchi, A. (xn) Ev. Sc.-Ind. 

15 (1883) 148-. 

Format's "Observatio" to Nikomachus' pro- 
position. Wertheim, G. Z. Mth. Ps. 43 

(1898) (H.-lt. Ab.) 41-. 

theorem and an Arabian MS. Kummer, E. E. 
N. A. Mth. 9 (1850) 386-. 

'works. Brassinne, E. Toul. Mm. Ac. 3 
(1853) 1-. 

Ferrari-Cardan, solution of reduced equation of 
4th order. Hunrath, K. Z. Mth. Ps. 30 
(1885) (H.-lt. Ab.) 41-. 

Fibonacci, algebraic operations wrongly at- 
tributed to. Chasles,M. C. E. 12 (1841) 741-. 



0010 History 

Fibonacci's treatise on algebra. Gerhardt, C. I. 
Grunert Arch. 2 (1842) 423-. 

"Fihrist" of Ibn Abu Ya'kub an-Nadim, bib- 
liographical notices of mathematicians in. 
Suter, H. Z. Mth. Ps. 37 (1892) (Suppl.) 
1-; 38 (1893) (H.-lt. Ab.) 126-. 

Florentine problem (aenigma Florentinum). 
Drobisch, M. W. Leip. Ab. Mth. Ps. 1 
(1852) 431-. 

Forcadel, Pierre, circa 1560. Fantes, . Toul. 
Ac. Sc. Mm. 6 (1894) 282- ; 7 (1895) 316- ; 
8 (1896) 361-. 

Fourier, Jean Baptiste Joseph. Arago, D. F. J. 
Par. Mm. de PI. 14 (1838) Ixix- ; A. C. 67 
(1838) 337- ; Smiths. Ep. (1871) 137-. 

series, history of. Gibson, G. A. Edinb. 
Mth. S. P. 11 (1893) 137-. 

Fourier's statistical tables. De Morgan, A. I. 

Act. J. 14 (* 1869) 89-. 
Fractional arithmetic in middle ages. Guerard, 

. Liouv. J. Mth. 3 (1838) 483-. 
Fractions, history of conception and treatment. 

Bobynin, V. V. Bb. Mth. (1896) 97-. 
French mathematical progress since 1830. 

Dupin, C. C. E. 1 (1835) 564-. 
Galileo Galilei. Favaro, A. Yen. I. Mm. 24 

(1891) 430 pp. 
, letter. Duhamel, J. M. C. C. B. 69 

(1869) 231-. 
, and the mathematicians of the Boman 

College, 1611. Govi, G. [1873] Em. E. 

Ac. Line. At. 2 (1875) 230-. 
, six letters. Govi, G. Ev. Sc. 33 (1884) 85-. 
Gauss and Bolyai, W. (F.), correspondence. 

Stdckel, P. Gott. Nr. (1897) 1-. 
, , . Konig, G. Mag. Tud. 

Ak. Ets. 10 (1899) 617-. 

, and J., correspondence (non- 
Euclidean geometry). Stdckel, P., & Engel, 

F. Mth. A. 49 (1897) 149-. 

on elliptic functions. Pepin, T. Em. N. 
Line. Mm. 9 (1893) (Pt. 2) 1-; 10 (1894) 

and Germain, correspondence. Genocchi, A. 
[1880] Tor. Ac. Sc. At. 15 (1879) 795-. 

, influence on geometrical ideas of Lobachev- 
skii. Vasil'ev, A. V. (xn) [1883] Kazan 
S. Nt. (Ps.-Mth.) P. 2 (1884) 9-. 

, . Relngardt, N. V. (xn) 

[1883] Kazan S. Nt. (Ps.-Mth.) P. 2 (1884) 

Gauss's investigations in elliptic functions. 

Gilnther, P. Gott. Nr. (1894) 92-. 
Gauss, letter. - Jonquieres, de. C. B. 122 

(1896) 829-. 
, letter to Gerling. Stdckel, P. Gott. Nr. 

(1896) 40-. 
, unpublished letter. Jonquieres, de. C. 

E. 122 (1896) 857-. 
Geodesy of Chaldeans. Oppert, J. As Fr C 

E. (1896) (Pt. 1) 133-. 
Geodetic lines, history. Stdckel, P. Leip. 

Mth. Ps. B. 45 (1893) 444-. 
Geometers, methods of ancient. Flauti, V. 

Nap. At. Ac. Sc. 1 (1852-54) 17-. 
Geometric solution of problems of 2nd degree 

before Euclid. Tannery, P. Bordeaux S 

Sc. Mm. 4 (1882) 395-. 



History 0010 



Geometrical character of ancient astronomy. 
Mansion, P. Z. Mth. Ps. 44 (1899) (Suppl.) 
275-. 

theories, past and present of important. 
Loria, G. Tor. Ac. Sc. Mm. 38 (1888) 
327-. 

Geometry and analysis at different periods. 
Zeuthen, . Sk. Nf. F. (1886) 44-. 

of the ancients, in particular an axiom of 
Archimedes. Stolz,O. Mth. A. 22 (1883)504-. 

with circle of fixed radius. Kutta, W. M. 
Ac. Nt. C. N. Acta 71 (1898) 69-. 

, development of methods and ideas, fca- 

zarski, . Kosmos (Lw.) 14 (1889) 271-. 
, of synthetic from Monge to 1847. 

Kotter, E. D. Mth. Vr. Jbr. 5 (1901) (Heft 

2) xxviii + 486pp. 
, infinitesimal, Pascal's works on. Delegue, . 

Dunkerque Mm. S. Encour. 14 (1869) 137-. 

of Kepler and Newton. Taylor, C. Camb. 
Ph. S. T. 18 (1900) 197-. 

Le Clerc and Ozanam. Graf, J. H. Z. 

Mth. Ps. 44 (1899) (Suppl.) 113-. 

in n dimensions, history and present state. 
Schlegel, V. Lpldina. 22 (1886) 92-, 108-, 
133-, 149-, 160- ; Ens. Mth. 2 (1900) 77-. 

of Polifilo. Barca, A. Padova Mm. Ac. 
(1809) 222-. 

triangle. (Euler.) Mackay, J. S. Edinb. 

Mth. S. P. 4 (1886) 51-. 
. (Historical sketch.) Vigarie, E. 

As. Fr. C. B. (1889) (Pt. 2) 117-. , 
triangles in 1890. Vigarie, E. Fschr. 

Mth. (1891) 38. 
Georgius de Hungaria, arithmetic of, 1499. 

Szily, C. von, & Heller, A. [1894] Mth. Nt. 

B. Ung. 12 (1895) 134-. 

German algebra (Coss) of 15th and 16th cen- 
turies. Treutlein, P. Z. Mth. Ps. 24 (1879) 
(Suppl.) 1-. 

, history. Wappler, E. Z. Mth. Ps. 44 

(1899) (Suppl.) 537-. 

arithmetical problems, old. Curtze, M. 
Bb. Mth. (1895) 110-. 

mathematics. Herwart ab Hohenburg's 
"Tabulae Arithmeticae irpoo-fla^atpeo^wj uni- 
versales," (1610). Glaisher, J. W. L. [1875] 
Camb. Ph. S. P. 2 (1876), 386-. 

universities, 17th cent., mathematics at the. 
Bartholomeei (Dr). Z. Mth. Ps. 13 (1868) 
(Suppl.) 1-. 

Germany, history of algebra in. Gerhardt, 

C. J. Berl. Mb. (1867) 41- ; (1870) 141-. 

mathematical teaching in, history. Giinther, 
S. Ens. Mth. 2 (1900) 237-. 

Gompertz, unfair suppression of acknowledg- 
ment to. De Morgan, A. Assur. Mg. 9 
(*1861) 86-. 

Graeco-Egyptian arithmetic. Loria, G. Bb. 
Mth. (1893) 79- ; G. Mt. 32 (1894) 28-. 

papyrus of the VII. IX. century, treating 
mainly of fractions. Bobynin, W. W. [V. V.] 
Fschr. Mth. (1895) 47-. 

Graeco-Indian researches. Cantor, M. Mil. I. 

Lomb. Ed. 9 (1876) 818-. 
Graeco-Italian Golden Synthesis' f rom MS. of 

Viviani. Ferroni, P. Mod. Mm. S. It. 19 

(1821) 187-. 



0010 History 



Greek Mathematics. 



History 0010 



Grassmann's "Ausdehnungslehre." Schlegel, 
V. Z. Mth. Ps. 41 (1896) (H.-lt. Ab.) 1-, 41-. 

Greek Mathematics. 

Aegidius de Columna. Steinschneider, M. Bb. 

Mth. (1891) 113-. 
Analysis, ancient Greek compared with modern. 

Matthes, C. J. Leijd. A. Ac. (1832-33), 



Anaritius, commentary on the elements of 

Euclid. Mansion, . Brux. S. Sc. A. 24 

(1900) (Ft. 1) 47-. 
Apollonius, " Conica " Book V, problem. Dro- 

bisch, M. W. Leip. B. 8 (1856) 103-. 
, conies. Hausel, . Liouv. J. Mth. 3 

(1858) 153-. 
, . Milne, J.J. Mth. Gz. No. 6 (1895) 49-. 



Greek Mathematics, continued 

Aristarchus of Samos. Tannery, P. Bordeaux 

S. Sc. Mm. 5 (1883) 237-. 
Aristotle, on a construction for parallels. Heath, 

T. L. Z. Mth. Ps. 44 (1899) (Suppl.) 153-. 
, difference between natural philosophy 

and mathematics. Dutordoir, . Brux. S. 

Sc. A. 24 (1900) (Pt. 1) 52-. 
, geometrical theorem in. Heiberg, J. L. 

Kjtfb. Ov. (1888) 1-. 
Diophantus codex, a re-found. Gollob, E. Z. 

Mth. Ps. 44 (1899) (H.-lt. Ab.) 137-. 
and composition of numbers from 2 

squares. Jacobi, C. G. J. Berl. B. (1847) 

265-. 
, German translation, annotations. Nessel- 

mann, G. H. F. Z. Mth. Ps. 37 (1892) (H.- 
lt. Ab.) 121-, 161-. 



, fragments. Tannery, P. Bll. Sc. Mth. As. , methods of calculation of irrational square 



5 (1881) (Pt. 1) 124-. 
, Inclinations. Flauti, V. [1850] Mod. S. 

It. Mm. 25 (1852) 223-. 
, , Bk. I., solution of problem in. Sangro, 

G. Nap. At. Ac. 2 (1825) 45-. 
, , , IV. Giannattasio, F. 

Nap. At. Ac. 2 (1825) 317-. 
, lost works on irrationals (Wopcke). Chasles, 

M. C. R. 37 (1853) 553-. 
, , reconstructed from Arabian MS. 

Woepcke, F. Par. Mm. Sav. Etr. 14 (1856) 

658. 
, problems and porismatic developments. 

Gardiner, M. Viet. T. E. S. 5 (1860) 19-. 
Archimedes, ancient criticism of a demonstra- 
tion of. Tannery, P. [1881] Bordeaux S. 

Sc. Mm. 5 (1883) 49-. 

and conies. Heiberg, J. L. Z. Mth. Ps. 25 
(1880) (H.-lt. Ab.) 4l-. 

, cyclometry. Hultsch, F. Z. Mth. Ps. 39 

(1894) (H.-lt. Ab.) 121-, 161-. 
, De numero arena. Chasles, M. C. R. 14 

(1842) 547-. 
.Ephodikon. Schmidt, W. Bb. Mth. 1 (1900) 

13 . 
, Greek manuscripts used in translation by 

W. von Moerbek. Heiberg, J. L. Z. Mth. 

Ps. 37 (1892) (H.-lt. Ab.) 81-. 

: ' ' Loculus Archimedius ' ' or the ' ' Synte- 
machion," publication of translation from 
two Arabic MSS. Suter, H. Z. Mth. Ps. 44 
(1899) (Suppl.) 491-. 

, measurement of circle. Tannery, P. Bor- 
deaux S. Sc. Mm. 4 (1882) 313-. 

, new studies. Heiberg, J. L. Z. Mth. Ps. 
34 (1889) (Suppl.) 1-. 

and problem of oxen. Amthor, A.,& Krum- 
biegel, B. Z. Mth. Ps. 25 (1880) (H.-lt. Ab.) 
121-, 153-. 

. Tannery, P. Bll. Sc. Mth. 

As. 5 (1881) (Pt. 1) 25-. 
, solution of cubic. Zeuthen, H. G. Bb. 

Mth. (1893) 97-. 
, theorem for the surface of a cylinder. 

Cayley, A. Mess. Mth. 13 (1884) 107-. 
, theorems. Heiberg, J. L. Z. Mth. Ps. 24 

(1879) (H.-lt. Ab) 177-. 
, treatment of arithmetic progression. Gibson, 

G. A. Edinb. Mth. S. P. 16 (1898) 2-. 



roots. Schoenborn, W. Z. Mth. Ps. 30 (1885) 

(H.-lt. Ab.) 81-. 
, polygonal numbers, treatise, concluding 

proposition. Wertheim, G. Z. Mth. Ps. 42 

(1897) (H.-lt. Ab.) 121-. 
, problems of, proofs. Zeuthen, H. G. (xn) 

Ts. Mth. 6 (1876) 168-, 181- ; 6 (1882) 97-; 

1 (1883) 145- ; Fschr. Mth. (1884) 32. 
, Psellus on. Tannery, P. Z. Mth. Ps. 37 

(1892) (H.-lt. Ab.) 41-. 
, work. Tannery, P. Bb. Mth. (1887) 37-, 

81-, 103- ; (1888) 3-. 
Euclid, Bk. I. 32. Corollary. Tucker, R. Nt. 

63 (1900-01), 58. 
, . . Allman, G. J. [1900] Nt. 

63 (1900-01) 106-. 
, . . Eumorfopoulos, S. [1900] 

Nt. 63 (1900-01) 157. 
, X., equations of 4th order. Christensen, 

S.A. Z. Mth. Ps. 34 (1889) (H.-lt. Ab.) 201-. 
, XII., and Archimedes on measurement 

of circle, &c. Ovidio, E. d'. G. Mt. 9 (1871) 

122-. 
and his century. Cantor, M. Z. Mth. Ps. 

12 (1867) (Suppl.) 1-. 
, porisms. Chasles, M. Quetelet Cor. Mth. 

10 (1838) 1-. 
, . Breton [de Champ-], P. C. B. 29 (1849) 

479- ; Liouv. J. Mth. 2 (1857), 185-. 
, . Cantor, M. Schlomilch Z. 2 (1857) 17-. 
, . Breton [de Champ], P. Liouv. J. 

Mth. 3 (1858) 89-. 
, , reply to Breton. Chasles, M. C. R. 51 

(1860) 1043-. 
, , restoration. Chasles, M. C. R. 48 

(1859) 1033- ; 50 (1860) 940, 997, 1007-. 
, , . Wilkinson, T. T. [1867] Manch. 

Lt. Ph. S. P. 7 (1868) 68-. 
, postulates and axioms. Mansion, P. Brux. 

S. Sc. A. 14 (1890) (Pt. 2) 35-. 
, problems, MS. in library of Royal Gym., 

Thorn. Curtze, M. Z. Mth. Ps. 13 (1868) 

(Suppl.), 45-. 
, translation from Arabic into Latin by 

Adelhard of Bath, according to MSS. at 

Erfurt. Weissenbom, H. Z. Mth. Ps. 25 

(1880) (Suppl.) 141-. 
Euclid's elements, Arabic version. Heiberg, 

J. L. Z. Mth. Ps. 29 (1884) (H.-lt. Ab.) 1-. 



0010 History 

Greek Mathematics, continued 
Euclid's elements, Nasr ad-Din's edition. 
Suter, H. Bb. Mth. (1892) 3-. 

text, alterations. Vincent, A. J. H. N. 
A. Mth. 3 (1844) 5-. 

Grecian page-numbers and diametral numbers. 

Bergh, P. Z. Mth. Ps. 31 (1886) (H.-lt. Ab.) 

135. 
Greek abacus, methods of reckoning on. 

Nagl, A. Z. Mth. Ps. 44 (1899) (Suppl.) 

335-. 

arithmetic. Hawkes, H. E. N. Y. Am. 
Mth. S. Bll. 4 (1898) 530-. 

geometry. Treutlein, P. Z. Mth. Ps. 28 
(1883) (H.-lt. Ab.) 209-. 

, the golden period of. Loria, G. Tor. 

Ac. Sc. Mm. 40 (1890) 369-. 
, higher. Valat, . Bordeaux Act. Ac. 

Sc. 24 (1862) 223-. 

mathematical fragment in Bobbio, Cod. 
Ambrosianus. Heiberg, J. L. Z. Mth. Ps. 
28 (1883) (H.-lt. Ab.) 121-. 

mathematics, remarks on history. Sturm, 
A. Z. Mth. Ps. 44 (1899) (Suppl.) 485-. 

, surviving history. Heiberg, J. L. Kjtfb. 

Ov. (1896) 77-. 

methods of calculating square-root. Schoen- 
born, W. Z. Mth. Ps. 28 (1883) (H.-lt. Ab.) 
169-. 

Greeks, mathematical discoveries. Ofterdinger, 

L. F. Grunert Arch. 5 (1844) 102-. 
, theory of numbers among. Cantor, M. (n. 

Adds.) [1863] Heidi. Vh. Nt. Md. 3 (1862- 

63) 61-. 
Hero of Alexandria. Tannery, P. Bordeaux 

S. Sc. Mm. 5 (1883) 347-. 

, fragments preserved by Proclus. 

Tannery, P. Bll. Sc. Mth. As. 6 (1882) (Pt. 

1) 99-. 

, Greek arithmetic. Tannery, P. 
Bordeaux S. Sc. Mm. 4 (1882) 161-. 

, influence on 17th century. Schmidt, 

W. Z. Mth. Ps. 42 (1897) (Suppl.) 195-. 

, stereometry. Tannery, P. Bordeaux 

S. Sc. Mm. 5 (1883) 305-. 

, extraction of irrational cubic-roots. Wer- 
theim, G. Z. Mth. Ps. 44 (1899) (H.-lt. Ab.) 

, metrics, a fragment. Tannery, P. Z. Mth. 

Ps. 39 (1894) (H.-lt. Ab.) 13-. 
Lunes, quadrature, fragment of Eudemus. 

Tannery, P. Bordeaux S. Sc. Mm. 5 (1883) 

211-. 
, , and Hippocrates of Ohio. Tannery, P. 

Bordeaux S. Sc. Mm. 2 (1878) 179-. 
Pappus, Greek arithmetic. Tannery, P. Bor- 
deaux S. Sc. Mm. 3 (1880) 351-. 
, text, MSS. in Great Britain. Eigaud, 

S. P. Edinb. Ph. J. 7 (1822) 56-, 219-. 
, passage. Heiberg, J. L. Z. Mth. Ps. 23 

(1878) (H.-lt. Ab.) 117-. 

on progressions. Mackay, J. S. Edinb. 
Mth. S. P. 6 (1888) 48-. 

, theorem, restoration. Barnwell, C. F. 
Edinb. J. Sc. 6 (1832) 90-. 

Perspective, "Was it known to Greek geo- 
meters?" Taylor, C. [1880] Mess. Mth. 
10 (1881) 112-. 



Greek Mathematics. 



History 0010 

Greek Mathematics, continued 

Planudes, calculation book. Gerhardt, C. I. 

Berl. Mb. (1867) 38-. 
Plato's geometry in Meno and Pythagoras' 

parabola in Plutarch. Wex, F. C. Arch. 

Mth. Ps. 47 (1867) 131-. 
Platonic number. Dupuis, J. As. Fr. C. B. 

(1886) (Pt. 2), 135-. 

. Demme, C. Z. Mth. Ps. 32 (1887) (H.- 
lt. Ab.) 81-, 121-. 
Problem of Delos, solutions by Archytas and 

Eudoxus. Tannery, P. Bordeaux S. Sc. 

Mm. 2 (1878) 277-. 
Ptolemy, "De Analemmate." Heiberg, J. L. 

Z. Mth. Ps. 40 (1895) (Suppl.) 1-. 
, geometrical knowledge. Ottema, J. G. 

(vm) Amst. N. Ws. Ntk. Vh. 1 (1844) 235-. 
on ratio of diameter to circumference. Ter- 

quem, 0. N. A. Mth. 13 (1854) 253-. 
, theories of movements of the planets. 

Haebler, A. Z. Mth. Ps. 45 (1900) (H.-lt. 

Ab.) 161-. 
Pythagoras, mathematics of. Cantor, M. 

Heidi. Vh. Nt. Md. (1857-59) 164-. 
Boot extraction according to Hero. Curtze, 

M. Z. Mth. Ps. 42 (1897) (H.-lt. Ab.) 113-. 
Science in Ancient Greece. Loria, G. Mod. 

Ac. Sc. Mm. 10 (1894) 3- ; 11 (1895) 3-. 
Serenus of Antissa. Tannery, P. Bll. Sc. Mth. 

As. 7 (1883) (Pt. 1) 237-. 
, birthplace. Heiberg, J. L. Bb. Mth. 

(1894) 97-. 
Simplicius. Steinschneider, M. Bb. Mth. 

(1892) 7-. 
, commentary on Euclid's elements. Bes- 

thorn, E. 0. Bb. Mth. (1892) 65-. 
Spheres, homocentric, of Eudoxus, Calippus 

and Aristotle. Schiaparelli, G. V. [1874] 

Mil. I. Lomb. Mm. 13 (1877) 117-. 
Spherical trigonometry and Ptolemy. Schubert, 

F. T. [1796] St Pet. Ac. Sc. N. Acta 12 

(1801) 165-. 
Square roots, Archimedes' approximate values. 

Heilermann, H. Z. Mth. Ps. 26 (1881) (H.- 
lt. Ab.) 121-. 
, . Weissenborn, H. Z. Mth. Ps. 

28 1883) (H.-lt. Ab.) 81-. 
, . Hultsch, F. Gott. Nr. (1893) 

367-. 
, calculation, Archimedes. Zeuthen, H. G. 

Ts. Mth. 3 (1879) 145-. 
, , and Hero. Demme, C. Z. Mth. 

Ps. 31 (1886) (H.-lt. Ab.) 1-. 
, extraction in ancient Greece. Bobynin, 

V. V. Z. Mth. Ps. 41 (1896) (H.-lt. Ab.) 

193-. 
Stobaeus on series. Bienayme, . C. B. 71 

(1870) 460-. 
Tactions of Apollonius, modern solution. Bren- 

necke (Dr). B. A. Bp. (1860) (Pt. 2) 4. 
Thales and geometry of Egyptians, ancient 

references. Hugo, L. C. B. 108 (1889) 767-. 
Work of Greeks in development of mathe- 
matics. Bobynin, V. V. Bb. Mth. (1892) 1-. 



Gylden's scientific methods. Bohlin, K. Acta 
Mth. 20 (1897) 397-. 



10 



0010 History 

Hamburg Math. Ges., Dutch members, history. 

Bierens de Haan, D. Hamb. Mth. Gs. Mt. 2 

(1890) (Festschr., Tl. 1) 79-. 
, history, 1690-1890. Bubendey, J. F. 

Hamb. Mth. Gs. Mt. 1 (1889) 8- ; 2 (1890) 

(Festschr., Tl. 1), 8-. 
Harriot's papers. Zach, F. X. von. Each Cor. 

7 (1822) 105-. 

. Eigaud, S. P. R. I. J. 2 (1831) 267-. 

Hebrew MS. of Ibn-Ezra, on arithmetic. Ter- 

quem, 0. Liouv. J. Mth. 6 (1841) 275-. 
on geometry (Mischnath Hammidoth) in 

Munich library, translation. Schapira, H. 

Z. Mth. Ps. 25 (1880) (Suppl.) 1-. 
, notes on. Steinschneider, M. Bb. Mth. 

(1893) 73-. 
Helmholtz's investigations on the fundamental 

principles of mathematics and mechanics. 

Koenigsberger, L. [1895] Smiths. Rp. (1896) 

93-. 
Historical notes. Luca, F. de. II Progresso, 

1 (1832) 163- ; 2, 3-, 169- ; 3, 235-. 
. Hill, C. J. D. Sk. Nf. F. 5 (1847) 

360-. 
. Luca, F. de. II Giamb. Vico, 4 (1857) 

451-. 

. Baltzer, E. Leip. B. 17 (1865) 1-. 

. Cockle, (Sir) J. [1875] Manch. Lt. 

Ph. S. P. 15 (1876) 6-. 
History of e and TT. Dikstein, S. Kosmos 

(Lw.) 20 (1895) 359- ; Fschr. Mth. (1895) 56. 
Holland, history of mathematical and natural 

sciences in. Bierens de Haan, D. Amst. 

Ak. Vs. M. 8 (1874) 57-, 163- ; 9 (1876) 1-, 

90-, 322-; 10 (1876) 161- ; 12 (1878) 1-; 14 

(1879) 180- ; 16 (1881) 1-; 18 (1883) 218- ; 

19 (1884) 1-, 78-, 249-; 20 (1884) 102-, 197- ; 

1 (1885) 224-; 3 (1887) 69-; 4 (1888) 65-; 

6 (1889) 103- ; 9 (1892) 4-; Fschr. Mth. 

(1884) 21-; (1885) 12-; (1886) 10-; (1887) 

14; (1889) 12-. 
Hudde, Johannes, year of birth. Korteweg, 

D. J. Z. Mth. Ps. 41 (1896) (H.-lt. Ab.) 22-. 
Huygens, Christian. Bosscha, J. Rv. Sc. 4 

(1895) 609- ; Arch. Neerl. 29 (1896) 352-; 



Indian Mathematics. 



History 0010 

Imaginary roots, historical note. Haan, D. 
B. de. Amst. Vs. Ak. 8 (1858) 248-. 

Indeterminate equation ax + by = c, ancient pro- 
cess for solution in integers. Eodet, L. 
Par. S. Mth. Bll. 7 (1879) 171-. 

Indian Mathematics. 

Ahmes and Baudhayana, rules regarding quad- 
rature of circle. Demme, C. Z. Mth. Ps. 31 
(1886) (H.-lt. Ab.) 132-. 

Binomial theorem known to Hindoos. Burrow, 
E. As. Researches, 2 (1790) 487-. 

Hindu arithmetic. Burrow, E. As. Re- 
searches, 3 (1792) 145-. 

geometry. Oppermann, L. H. F. (xn) Ts. 
Mth. 1 (1871) 55-, 124-. 

quadrature of circle. Whish, C. M. [1832] 
As. S. T. 3 (1835) 509-. 

Indian calculation of the sine, and the word 
Kardaga. Woepcke, F. N. A. Mth. 13 (1854) 
386-. 

Mathematics in the East Indies. Delbos, L. 
Bll. Sc. Mth. 16 (1892) 93-; 17 (1893) 145-. 

Quadrilateral in circle whose parts are all 
rational. Terquem, 0. N. A. Mth. 5 (1846) 
636. 

Square-root approximation method known be- 
fore Alexander's conquest. Eodet, L. Par. 
S. Mth. Bll. 7 (1879) 98-, 159-. 

Trigonometrical tables of the Brahmins. Play- 
fair, J. [1795] Edinb. R. S. T. 4 (1798) 83-. 

Two problems by Bapu Deva Shastri. Hall, 
B. H. Silliman J. 11 (1851) 194-. 



Stolz, 0. 



Infinitesimal calculus and Bolzano. 

[1880] Mth. A. 18 (1881) 255-. 
, history of. Dickstein, S. Prace Mt.- 

Fiz. 10 (1899-1900) 178-. 
1 invention. Zeuthen, H. G. Kjtfb. Ov. 

(1895) 193-, 257-. 
, origin. Milhaud, G. [1900] N. Y. Am. 

Mth. S. Bll. 7 (1901) 157, 158. 
, . Cantor, M. [1900] N. Y. Am. 

Mth. S. Bll. 7 (1901) 158, 159-. 

Ciel et Terre 17 (1896-97), 173-, 202-, 289-. , principles, history. Critics of Lagrange's 

, , discoveries and documents published by ' ' Theorie des f onctions analy tiques. " Dtcfc- 

Chasles. Kaiser, F. Arch. Mth. Ps. 49 *tein, S. Z. Mth. Ps. 44 (1899) (Suppl.) 65-. 

, text books from Euler to present time. 

Bohlmann, G. D. Mth. Vr. Jbr. 6 (1899) 

(Heft 2) 91-. 
Infinitesimals, early history in England. De 

Morgan, A. (viAdds.) Ph. Mg. 4 (1852) 321-. 
Integral (1 + n cos <t>) r d<f>, MS. memoir on. 

Gauss, C. F. Gott. Nr. (1893) 617-. 
"Introduction Arithmetique " (de Gerase) 

Livre II, ch. 9 and 20. Martin, H. Torto- 

lini A. 8 (1857) 429-. 
Invariant theory, history of development and 

account of present condition. Meyer, F. D. 

Mth. Vr. Jbr. 1 (1892) 79-. 
"Invention nouvelle en 1'Algebre" (reproduc- 
tion of 16th century work by Albert Girard) . 

Bierens de Haan, D. N. Arch. Wisk. 11 

(1884) 83-. 
Irrational square-roots, calculation of, and the 

invention of continued fractions. Wertheim, 

G. Z. Mth. Ps. 42 (1897) (Suppl.) 147-. 



Kaiser, F. Arch. Mth. Ps. 49 

(1869) 81-. 
, Constantijn, and Descartes. Korteweg, D. J. 

Arch. Neerl. 22 (1888) 422-. 
Hypergeometric series, Gauss' works on, errors 

in. Simon, H. Z. Mth. Ps. 32 (1887) (H.- 

It.-Ab.) 99-. 
, history. Schulze, K. Hamb. Mth. Gs. 

Mt. 1 (1889) 110-. 
Imaginaries, geometric representation. Hoiiel, 

J. Bordeaux Mm. S. Sc. 5 (1867) i-. 
Imaginary elements in geometry, historical 

monograph on. Eamorino, A. G. Mt. 35 

(1897) 242- ; 36 (1898) 317-. 

numbers, history. StudniZka, F. J. Casopis 
13 (1884) 49-, 254- ; Fschr. Mth. (1884) 37-. 

quantities in analysis, development. Kiess- 
ling, K. J. Hamb. Mth. Gs. Mt. 1 (1889) 
24-. 

, history of theory. Beman, W. W. Am. 
As. P. (1897) 33-. 



11 



0010 History 

Irrationality of e and it, on early proofs of. 

Pringsheim,A. Munch. Ak. Sb. 28 (1899) 325-. 
Irrationals, quadratic, of ancients and their 

methods of development. Giinther, S. Z. 

Mth. Ps. 27 (1882) (Suppl.) 1-. 
Italian contributions to mathematics. Riccardi, 

P. Bologna Ac. Sc. Mm. 6 (1896-97) 755- ; 

7 (1897) 371-. 

mathematical works 1800-16. Anon. (vi. 
138.) Bb. It. 1 (1816) 225-, 358-; 2, 60-. 

sources for historico-mathematical know- 
ledge. Favaro, A. Bb. Mth. (1889) 113-. 

Jacobi's correspondence with Legendre. Jacobi, 
C. G. J. Bll. Sc. Mth. As. 8 (1875) 287- ; 
9 (1875) 38-, 51-, 126-. 

posthumous works. Lejeune-Dirichlet, G. 
Crelle J. 42 (1851) 91-. 

theorem, extension, priority claim. Meyer, 
U. H. Grunert Arch. 22 (1854) 474-. 

theta formulae, date and origin. Kronecker, 
L. Berl. Ak. Sb. (1891) 653-. 

Japan, history of mathematics in. Westphal, A. 

(xn) [1876] D. Gs. Ostas. Mt. 1 (1873-76) 

(Heft 9) 54-. 
Japanese arithmetic, use of geometry in. 

Berson, . Toul. Ac. Sc. Mm. 3 (1891) 268-. 

mathematics. Fujisawa, . [1900] N. Y. 
Am. Mth. S. Bll. 7 (1901) 69. 

Jaquemet, Pere, two letters. Marre de Marin, 
E.A. Bll. Sc. Mth. As. 4 (1880) (Pt. 1) 200-. 

Jewish mathematics. Steinschneider, M. Bb. 
Mth. (1893) 65-, 105- ; (1894) 37-, 79-, 99-; 

(1895) 19-, 43-, 97-; (1896) 32-, 77-, 109- ; 
(1897) 13-, 35-, 73-, 103- ; (1898) 5-, 33-, 
79-; (1899) 1-, 37-, 97-. 

(150150). Steinschneider, M. Z. 

Mth. Ps. 44 (1899) (Suppl.) 471-. 
Johann von Gemunden. Curtze, M. Bb. Mth. 

(1896) 4. 

Johannes de Lineriis, nationality. Curtze, M. 

Bb. Mth. (1895) 105-. 
Johannes de Muris, "Das Quadripartitum," 

and practical arithmetic in the 14th century. 

Nagl, A. Z. Mth. Ps. 34 (1889) (Suppl.) 

135-. 

Saxonia's commentary on Introductio 
Alcabitii. Steinschneider, M. Bb. Mth. 
(1891) 114-. 

Jordanus Nemorarius, certain algebra problems. 

Wertheim, G. Bb. Mth. 1 (1900) 417-. 
, "Tractatus de numeris datis." Treut- 

lein, P. Z. Mth. Ps. 24 (1879) (Suppl.) 125-. 
, . Curtze, M. [1880-91] 

Lpldina. 18 (1882) 26-; Z. Mth. Ps. 36 (1891) 

(H.-lt. Ab.) 1-, 41-, 81-, 121-. 
1 . Daublebsky von Sterneck, R. 

Mh. Mth. Ps. 7 (1896) 165-. 
Josephus Sapiens or Hispanus, Gerbert on. 

Weissenborn, H. Bb. Mth. (1893) 21-. 
Hispanus, Gerbert on. Curtze, M. 

Bb. Mth. (1894) 13-. 
(reply to Curtze). Suter, H. Bb. Mth. 

(1894) 84. 
Kepler's logarithms, and letters of Kepler. 

Frinch, . Grunert Arch. 24 (1855) 286-. 
Kochanski and Leibnitz, correspondence be- 
tween. Dickstein, S. Fschr. Mth. (1897) 

9-; Krk. Ak. (Mt.-Prz.) Rz. 13 (1898) I-/ 



History 0010 

Lagrange and Euler's correspondence. Cantor, 

M. Z. Mth. Ps. 23 (1878) (H.-lt. Ab.) 1-. 
, letters. Genocchi, A. Tor. Ac. Sc. At. 9 

(1874) 746-. 
, letters to Euler, published by Boncompagni. 

Genocchi, A. [1877] Tor. Ac. Sc. At. 12 

(1876) 350-. 
, , four. Lagrange, J. L. (x) Tor. Ac. 

Sc. At. 9 (1873-74) 756-. 
, works. Bertrand, J. J. Sav. (1869) 257-. 
Lancashire geometers. Wilkinson, T. T. 

Manch. Ph. S. Mm. 11 (1854) 123-. 

and ancient geometrical analysis. 
Wilkinson, T. T. Lane. T. Hist. S. 8 (1856) 
75-. 

Least squares method, historical note. Abbe, C. 
Am. J. Sc. 1 (1871) 411-. 

, history. Merriman, M. Des Moines 

Anal. 4 (1877) 33-, 140-. 

, priority claims. Gerling, C. L. Gott. 

Nr. (1861) 273-. 

Legendre, Adrien Marie. M., F. Bb. Un. 52 
(1833) 45-. 

Legendre 's correspondence with Jacobi. Le- 
gendre, A. M. Bll. Sc. Mth. As. 8 (1875) 
287-; 9 (1875) 38-, 51-, 126-. 

"Theory of numbers," error in. Dujardin, 
. C. B. 119 (1894) 843-, 934. 

Leibnitz, correspondence. Jacobi, C. G. J. 
Berl. B. (1850) 426-. 

on determinants. GerJiardt, K. I. Berl. 
Ak. Sb. (1891) 407-. 

MSS. published by Gerhardt. Weissenborn, H. 
Schlomilch Z. 1 (1856) 240-. 

and Pascal. Gerhardt, C. I. Berl. Ak. Sb. 
(1891) 1053-. 

, theorem; and a letter of Lagrange. 
Genocchi, A. Tor. At. Ac. Sc. 4 (1868-69) 
263-. 

Leibnitz's discovery of algorithm of higher 
analysis, 200th anniversary of. Gerhardt, 
C. I. Berl. Ac. Mb. (1875) 588-. 

Leo, Byzantine mathematician of 9th cen- 
tury. Heiberg, J. L. Bb. Mth. (1887) 33-. 

Leonardo da Vinci, geometrical constructions 
by. Cantor, M. Hamb. Mth. Gs. Mt. 2 
(1890) (Festschr., Tl. 1) 8-. 

Vinci's geometrical construction for 
ellipse. Rulf, W. Mh. Mth. Ps. 9 (1898) 
30-. 

Leonardo Pisano, life and works. Boncompagni, 
B. Bm. At. 5 (1851-52) 5-, 208-. 

, three of his writings published by Bon- 
compagni. Genocchi, A. Tortolini A. 6 
(1855) 161-, 218-, 273-, 345-. 

, . Terquem, O. 

Tortolini A. 7 (1856) 106-. 

, treatise on square numbers. Woepcke, 

F. Liouv. J. Mth. 20 (1885) 54-. 

, work on cubic equations. Woepcke, F. 

Liouv. J. Mth. 19 (1854) 401-. 

Pisano's "Liber Quadratorum," problems. 
Genocchi, A. Tortolini A. 6 (1855) 186-, 
251-. 

writings, and their relation to Arabian 

works. Woepcke, F. Km. At. 10 (1856-57) 
236-; 12 (1858-59)230-, 399-; 14 (1860-61) 
211-, 241-, 301-, 343-. 



12 



0010 History 

Letter "x," origin of denoting the unknown 

by. Wertheim, G. Z. Mth. Ps. 44 (1899) 

(H.-lt. Ab.) 48. 
Liber karastonis sive de statera. Steinschneider, 

M. (vm) [1862] A. Mt. 5 (1863) 54-. 
Liber trium fratrum. Kinkelin, H. Basel Vh. 

3 (1863) 511-. 

(9th century work on geometry). 
Curtze, M. Ac. Nt. C. N. Acta 49 (1887) 
105-. 

, proposition of an approximate cal- 
culation in. Vaux, C. de. Bb. Mth. (1898) 
1-. 

Lie, Marius Sophus, communications from, 
1869-71. Sylow, L. Christiania Skr. (Mth.- 
Nt. Kl.) (1899) No. 9, 15 pp. 

, , scientific work. Zorawski, K. Wiad. 

Mt. 3 (1899) 85-. 

Limits of error of 7- etc. deduced from the 
b 

known limits of error of a, b, respectively. 

Mehmke, R. Fschr. Mth. (1888) 1289-. 
Linear differential equations. Radelfinger, 

F. G. [1899] Wash. Ph. S. Bll. 14 (1906) 

21-. 
Lobacevskij as algebraist. Vasiliev, A. N. Y. 

Mth. S. Bll. 3 (1894) 231-. 
, centenary of birth, celebration at Imperial 

University, Kasan. Weyr, E. Casopis 25 

(1896) 1-; Fschr. Mth. (1896) 15. 
Logarithm of sum or difference, and solution 

of quadratic equation by circular functions, 

Cavalieri's methods, 1639. Govi, G. Em. 

R. Ac. Line. At. 3 (1876) (Pte. 2) 173-. 
Logarithmic tables, early history. Glaisher, 

J. W. L. Ph. Mg. 44 (1872) 291-, 500-. 

, , and their calculators. Glaisher, 
J. W. L. Ph. Mg. 45 (1873) 376-. 

, the first. Hejzlar, F. Casopis 3 (* 1874) 

49-. 
, progress to accuracy. Glaisher, J. W. L. 

As. S. M. Not. 33 (1873) 330-. 
Logarithms, Gaussian, origin. Bouniakowsky, 

V. [1862] St Pet. Ac. Sc. Bll. 5 (1863) 471-. 
, history, critique. Matzka, W. Grunert 

Arch. 34 (1860) 341-. 
, and literature. Gieswald, . Grunert 

Arch. 26 (1856) 316-. 
, , notes. Cajori, F. Z. Mth. Ps. 44 

(1899) (Suppl.) 31-. 
, notation of. Draenert, . D. Nf. Tbl. 

(*1876) (Suppl.) 173-. 
Logic, precursors in mathematical. Peano, G. 

Bv. Mt. 4 (1894) 120. 
, . Vacca, G. Ev. Mth. 6 (1896-99) 

121-. 
, . Gergonne, J. D. Ev. Mth. 6 

(1896-99) 183-. 
Longitude determination at sea, history. Gel- 

cich, E. Z. Mth. Ps. 44 (1899) (Suppl.) 105-. 
Malfatti's problem, history. Baker, M. [1877] 

Smiths. Misc. Col. 20 (1881) Art. 2, 113-. 

(Wash. Ph. S. Bll. 2 (1880).) 
MS. No. 14836 of the K. Hof- u. Staatsbiblio- 

thek, Miinchen. Curtze, M. Z. Mth. Ps. 40 

(1895) (Suppl.) 75-. 
MSB., some old. Wittstein, A. Z. Mth. Ps. 

40 (1895) (H.-lt. Ab.) 121-. 



History 0010 

Marci , Joannes Marcus (Jan Marck) . Studnidka, 
F. J. Bohm. Gs. Ws. Jbr. (1890) xxxii pp. 

Martinus Eex and his geometry. Dickstein, S. 
Fschr. Mth. (1895) 10. 

Mascheroni's geometry of the compass. Cay- 
ley, A. Mess. Mth. 14 (1885) 179-. 

Mathematical analysis, development of theories 
in, during 19th century. Picard, E. [1899] 
Wiad. Mt. 4 (1900) 173-. 

anecdotes. Ferroni, P. Verona S. It. Mm. 
7 (1794) 319-. 

historical research, purpose and results of 
recent. Gilnther,. D.Nf.Tbl. (*1875) 130-. 

history, present problems. Loria, G. [1892] 
Bb. Mth. (1893) 39-. 

instruments of Count G. Suardi of Brescia. 
Gelcich, E. Z. Mth. Ps. 30 (1885) (H.-lt. 
Ab.) 1-. 

knowledge previous to science. Bobynin, 
V. V. Bb. Mth. (1889) 104-. 

papyrus in Greek language. Cantor, M. 
Z. Mth. Ps. 38 (1893) (H.-lt. Ab.) 81-. 

and physical disputations at Leipzig, 1512- 
26. Suter, H. Bb. Mth. (1889) 17-. 

science, history (Giinther) . Favaro, A . 

Yen. I. At. 3 (1877) 913-. 

science in Eussia, development. Bobynin, 
W. W. [V. V.-]. Fschr. Mth. (1890) 3. 

sciences, progress of. Zegers, J. Chile A. 
Un. (1852) 35-. 

, among European nations. Bobynin, 

V. V. Bb. Mth. (1892) 110-. 
, since 1789. Delambre, J. B. J. Par. 

Mm. de PI. (1808) (H.) 171-. 

theory of life assurance (historical). Samot, 
D. N. Arch. Wisk. 5 (*1879) 35-. 

Mathematics, development from the most remote 

times to 15th century. Vashchenko-Zakhar- 

chenko, M. [1882] Bordeaux S. Sc. Mm. 5 

(1883) 259-. 
, historiography of . Cantor, . [1900] N. Y. 

Am. Mth. S. Bll. 7 (1901) 57-. 
, history. Piani, D. (vm) Bologna Opusc. 

Sc. N. Col. (1824) 191-. 
, . Enestrom, G. (xii) Ts. Mth. 3 

(1879) 113-, 161-. 
, , in antiquity, series of articles. Tannery, 

P. Bll. Sc. Mth. As. 8 (1884); Bll. Sc. 

Mth. 9 (1885); 10 (1886); 11 (1887). 
, , applied to the solution and statement 

of some questions. Bobynin, W. W. [V. V.]. 

Fschr. Mth. (1892) 77. 
, by Boncompagni. Chasles, M. C. E. 

34 (1852) 889-. 
, , contribution to. Wappler, E. Z. Mth. 

Ps. 34 (1889) (Suppl.) 147- ; 45 (1900) (H.-lt. 

Ab.) 7-. 
, for high-schools. Enestrom, G. (xn) 

Ts. Mth. 4 (1880) 62-. 
, , in Middle Ages, contributions to. 

Heiberg, J. L. Z. Mth. Ps. 35 (1890) (H.-lt. 

Ab.) 41-, 81-. 
, , a question of. Eubini, R. G. Mt. 17 

(1879) 149-. 
, , recent researches. Gilnther, S. D. Nf. 

[B.] (1877) 83-. 
, , . Enestrom, G. Bb. Mth. (1887) 

3 



13 



0010 History 

Mathematics, &c., history, proposed method of 

writing. Luca, F. de. II Giamb. Vico 

4 (1857) 451-. 
, present state of some branches. Smith, 

H. J. S. [1876] L. Mth. S. P. 8 (1876-77) 

6. 
, use of history in teaching. Heppel, G. Nt. 

48 (1893) 16-. 
Matthew Stewart's theorem. Mackay, J". S. 

Edinb. Mth. S. P. 10 (1892) 90-. 
Maurolico, Francesco, on Archimedes and 

Apollonius. Flauti, V. Nap. Ed. 5 (1856) 

112-. 
, , arithmetic, historical notes. Fontana, 

M. Bologna Mm. I. It. 2 (1808) 275-. 
Meaning, traditional, of word "geometry." 

Zeuthen, H. G. Kjrfb. Ov. (1893) 330-. 
Mediaeval translations of Euclid's elements. 

Curtze, M. Bb. Mth. (1896) 1-. 
Middle ages, progressions in. Curtze, M. Bb. 

Mth. (1895) 113-. 
Modern organization of mathematics. Gal- 

deano, Z. G. de. Fschr. Mth. (1899) 68. 
Mobius and Weiske, recollections of. Baltzer, 

E. Leip. Mth. Ps. B. 37 (1885) 1-. 
Monge, Gaspard, life and works. Mercadier, . 

Par. Mm. de PI. 24 (1854) (H.) 1-; Bv. Sc. 

1 (1894) 779-. 
Mortality tables before Halley, history. Enes- 

trom, G. Stockh. Ofv. (1896) 157- ; Fschr. 

Mth. (1896) 187. 
Moscow Math. Soc., historical sketch. Mlod- 

zeevskij, B. K. [1894] Bee. Mth. (Moscou) 

18 (1896) xxx-. 
Multiplication, abridged. Curtze, M. Z. Mth. 

Ps. 40 (1895) (H.-lt. Ab.) 1-. 
Napier, John, biography and works. Gravelaar, 

N. L. W. A. Amst. Ak. Vh. (Sect. 1) 6 

(1899) No. 6, 159 pp. 
, , inventor of logarithms. Biot, J. B. 

J. Sav. (1835) 354-; Con. des Temps (1838) 

, , review of memoirs on. Biot, J. B. J. 

Sav. (1835) 257-. 
Nasr ad-Din and Begiomontanus. Braunmiihl, 

A. von. Ac. Nt. C. N. Acta 71 (1898) 31-. 
National mathematics, memorials. Iznoskov, I. 

Kazan S. Nt. (Ps.-Mth.) P. 3 (1885) 88-. 
Negative numbers, introduction. Fouche, M. 

N. A. Mth. 12 (1893) 164-. 
Newton, (Sir) Isaac, Brewster's Life of. Biot, 

J. B. J. Sav. (1832) 193-, 263-. 
, , Memoirs of. Biot, J. B. J. Sav. 

(1855) 589-, 662-. 
and his correspondence with Cotes. Biot, 

J. B. J. Sav. (1852) 133-, 217-, 269-. 
Pascal, forged correspondence between. 

Chasles, M. C. B. 65-72 (1867-71) passim. 
, . Brewster, (Sir) D. C. B. 

65 (1867) 261-, 537-, 653-, 717-, 769-, 770-, 

825-, 925-. 
. . Chevreul, M. E. C B 69 

(1869) 305-. 
, portraits of. Crompton, S. [1866-67] 

Manch. Lt. Ph. S. P. 6 (1867) 1-; 7 (1868) 

3. 
Newton's classification of cubic curves Ball 

W. W. E. L. Mth. S. P. 22 (1891) 104-. ' 



History 0010 

Newton's influence on modern geometry. 
Graham, E. II. Nt. 42 (1890) 139-. 

Principia, a section of, in relation to modern 
geometry. Taylor, C. Camb. Ph. S. P. 3 
(1880) 359-. 

, singular passage in. Tait, P. G. Edinb. 

B. S. P. 13 (1886) 72-. 

Nine-point circle, history. Mackay, J. S. 

Edinb. Mth. S. P. 11 (1893) 19-. 
Nipsus, rule, and new theorem. Poinsot, L. 

C. B. 28 (1849) 581-. 

Non-Euclidean geometry, brief historical sketch. 

Prosper, V. E. Fschr. Mth. (1893-94) 78. 
, progress in. Halsted, G. B. Am. As. P. 

(1899) 53-. 
Notation, systems used by various races. Hum- 

boldt, F. H. A . von. Crelle J. 4 (1829) 205-. 
Numerals, earliest history. Cantor, M. (vi. 

Adds.) D. Nf. Vsm. B. 34 (1858) 135-. 
, transition from Eoman to Arabic. Herford, 

B. Manch. Lt. Ph. S. P. 12 (1873) 91-. 
Numeration of ancient Mexicans. Simeon, . 

Mex. Arch. Com. Sc. 3 (1867) 523. 
, origin. Savary, A. Par. Tr. S. Amat. 

2 (1808) 71-. 

Oppermann and Steen. Zeuthen, H. G. N. 

Ts. Mth. 10 (A) (1899) 33-; Fschr. Mth. 

(1899) 80. 
Optic and catoptric anamorphoses, history. 

Euoss, H. Z. Mth. Ps. 39 (1894) (H.-lt. Ab.) 

Oresme, Nicole, works. Curtze, M. Bll. Sc. 
Mth. As. 6 (1874) 57-. 

Oriental and occidental mathematics, connec- 
tion. Giinther, S. Lpldina. 13 (1877) 38-. 

origin of ir = 3. Mahler, E. Z. Mth. Ps. 
27 (1882) (H.-lt. Ab.) 207-. 

Painvin, L., works. Bll. Sc. Mth. As. 9 (1875) 
188-. 

Paoli, Pietro. Mod. Ac. Sc. Mm. 1 (1898) 105-. 

Pappus and Kepler, relation between. Giinther, 
S. Bb. Mth. (1888) 81-. 

Papyri recently discovered, dealing with mathe- 
matics. Heiberg, J. L. Kjtfb. Ov. (1900) 

Pascal denies authorship of certain papers pre- 
sented to Academy. Breton (de Champ), . 

C. B. 68 (1869) 710-, 862-, 969-. 

and Lalouvere. Tannery, P. Bordeaux S. 
Sc. Mm. 5 (1890) 55-; 4 (1894) 251-. 

Pascal's "Essais pour les coniques." Mac- 
donald, W. J. Edinb. Mth. S. P. 2 (1884) 
19-. 

letters, supposed. Lindeldf, L. L. [1867] 
Helsingf. Ofv. 10 (1868) 17-. 

MS. notes. Faugere, . C. B. 65 (1867) 
202-, 340-, 455-, 643-, 702; 67 (1868) 497. 

. Benard, . C. E. 65 (1867) 203-. 

Persian work on mathematics and astronomy. 

Tytler, J. As. S. J. 4 (1837) 254-. 
Petrus de Dacia and his writings. Enestrom, G. 

Stockh. Ofv. (1885) No. 3, 15-, No. 8, 65-; 

(1886) 57-; Fschr. Mth. (1885) 4-. 
Pitiscus: " Thesaurus mathematicus. " Burck- 

hardt, F. [1868] Basel Vh. 5 (1873) 159-. 
Pitiscus' " Trigonometria " (A.D. 1595), account 

of. Gravelaar, N. L. W. A. N. Arch. Wisk. 

3 (1898) 253-; Fschr. Mth. (1898) 32-. 



14 



0010 History 

Plane curves, history of investigation on. Loria, 

G. Wiad. Mt. 2 (1898) 203-. 
, Boberval's method. Geer, P. van. N. 

Arch. Wisk. 11 (1884) 28-; Fschr. Ps. (1884) 

(Ab. 1) 217-. 
Platonic number. Giinther, S. Lpldina. 18 

(1882) 149-. 
Pliny, remarks on passage in. Giinther, S. 

Arch. Mth. Ps. 55 (1873) 147-. 
Pliicker, works. Bertrand, J. J. Sav. (1867) 

269-. 
Polish mathematical literature, 1873-92. Dik- 

stein, S. Kosmos (Lw.) 20 (1895) 352-. 
Polyhedra and numerals, history. Lindemann, 

F. Munch. Ak. Sb. 26 (1897) 625-. 
Popular account of new fields of mathematics. 

Miller, G. A. Science 11 (1900) 528-. 
Porism, old. Davies, T. S. Mathematician 

3 (1850) 75-, 140-, 225-, 311- ; (Suppl.) 42-. 
Poristic triangles and polygons, historical notes. 

Mackay, J. S. Edinb. Mth. S. P. 5 (1887) 

62-. 
"Practica Geometries" (12th century tract). 

Curtze, M. Mh. Mth. Ps. 8 (1897) 193- ; 9 

(1898) 266-. 

Problem by V. Viviani. Geoghegan, E. Nt. 38 

(1888) 78. 
Problems on numbers from Fermat, some. 

Pepin, T. Bm. N. Line. Mm. 8 (1892) 85-. 
, some inverted (an old arithmetic book). 

C., R. A. Educ. Times 48 (1895) 29-. 
Projectile curve, discovery of parabolic form. 

WoMwill, E. Z. Mth. Ps. 44 (1899) (Suppl.) 

577-. 
Properties of figure composed of a triangle and 

the squares on its sides. Mackay, J. S. 

Edinb. Mth. S. P. 6 (1888) 2-. 
Prosthaphasresis method in trigonometry, his- 
tory. Braunmuhl, A. von. Z. Mth. Ps. 44 

(1899) (Suppl.) 15-. 

Quadratic irrationalities, approximate calcula- 
tion, history. Hunrath, K. Z. Mth. Ps. 33 

(1888) (H.-lt. Ab.) 1-. 

residues, historical account of law of reci- 
procity. Baumgart, 0. Z. Mth. Ps. 30 

(1885) (H.-lt. Ab.) 169-, 241-. 
, study. Pepin, T. Bm. N. Line. Mm. 

16 (1899) 229-. 
Quadratum geometricum, anonymous work on. 

Curtze, M. Z. Mth. Ps. 40 (1895) (H.-lt. Ab.) 

161-. 
Quadratures before integral calculus, especially 

Format's. Zeuthen, H. G. Kjtfb. Ov. (1895) 

37. 
Quaternions, Gauss' claim to invention of. 

Tail, P. G. [1899] Edinb. E. S. P. 23 (1902) 

17-. 
, Klein's view of. Knott, C. G. [1899] 

Edinb. B. S. P. 23 (1902) 24-. 
Quintic equation, history of theory. Pierpont, J. 

Mh. Mth. Ps. 6 (1895) 15-. 
Babbis, irrationalities. Mahler, E. Z. Mth. 

Ps. 29 (1884) (H.-lt. Ab.) 41-. 
Baoul de Laon, arithmetical treatise. Nagl, A. 

Z. Mth. Ps. 34 (1889) (Suppl.) 85-. 
Bates of interest in ancient and modern times. 

Hodge, W. B. Assur. Mg. 6 (*1857) 301- ; 

7 (*1858) 311- ; 8 (*1860) 68-; 9 (*1861) 61-. 



History 0010 

Beckoning of chances (reproduction of 16th 
century work by Benedict Spinoza). Bier ens 
de Haan, D. N. Arch. Wisk. 11 (1884) 75-. 

Bheticus, "Canon Doctrines Triangulorum " 
and Vieta's "Canon Mathematicus." Hun- 
rath, K. Z. Mth. Ps. 44 (1899) (Suppl.) 
211-. 

Bhind papyrus, interpretation. Favaro, A. 
Mod. Ac. Sc. Mm. 19 (1879) 89-. 
2 

on reducing to fractions with 

numerator 1. Bobynin, V. V. Bb. Mth. 

(1890) 109-. 
, a table in the. Mansion, . Brux. S. 

Sc. A. 12 (1888) (Ft. 1) 44-. 
Bhythmomachy. Wappler, E. Z. Mth. Ps. 

37 (1892) (H.-lt. Ab.) 1-. 
Bichelot's posthumous papers, extract. Konigs- 

berger, L. Bpm. Mth. 1 (1877) 191-, 340-. 
Biemann and his significance for modern 

mathematics. Klein, F. D. Nf. Vh. (1894) 

(Th. 1) 57-. 

Bobertus (? Johannes) Anglicus and his quad- 
rant. Steinschneider, M. Bb. Mth. (1896) 

102-. 
. Tannery, P. Bb. Mth. 

(1897) 3-. 

, " Tractatus Quadrantis," Germ, 
transl., 1477. Curtze, M. Z. Mth. Ps. 44 
(1899) (Suppl.) 41-; 45 (1900) (H.-lt. Ab.) 41-. 

Buffini, Paolo, and the theory of groups. 

Burkhardt, H. Z. Mth. Ps. 37 (1892) 

(Suppl.) 119-. 

Bussia, mathematical teaching, history. Boby- 
nin, V. V. Ens. Mth. 1 (1899) 77-. 
, sketch of development of physico-mathe- 

matical sciences in. Bobynin, V. V. [1886] 

Fschr. Mth. (1887) 2. 
Saccheri, a precursor of Legendre and Lobacev- 

skij. Beltrami, E. Bm. B. Ac. Line. Bd. 

5 (1889) (Son. 1) 441-. 
, Lobacevskij. Vasiljev, A. V. 

Kazan S. Ps.-Mth. Bll. 3 (1893) (Prot.) 53-. 
, researches on postulate of parallels. 

Mansion, P. Brux. S. Sc. A. 14 (1890) 

(Pt. 2) 46-. 
Scheubel, Johannes, German algebraist of 16th 

century. StaigmiJller, H. Z. Mth. Ps. 44 

(1899) (Suppl.) 429-. 

Schlafli (Ludwig) and Steiner (Jakob), corre- 
spondence between. Graf, J. H. Bern Mt. 

(1896) 61-. 
" Seqt," so-called, of Egyptian mathematicians. 

Cantor, M. Wien Ak. Sb. 90 (1885) (Ab. 2) 

475-. 
Signs of arithmetical operations, origin of some. 

Le Paige, C. Brux. S. Sc. A. 16 (1892) 

(Pt. 2) 70-. 
, + and - , history. De Morgan, A. [1864] 

Camb. Ph. S. T. 11 (Pt. 1) (1866) 203-. 
, , . Clifton, E. B. [1865] Camb. 

Ph. S. T. 11 (Pt. 1) (1866) 213-. 
, invention, and use by Leonardo da 

Vinci. De Morgan, A. (vi. Adds.) Ph. Mg. 

20 (1842) 135-, 230-. 
+ and -, use to denote "plus" and 

"minus." Enestrom,G. Stockh. Ofv. (1894) 

243-; Fschr. Mth. (189394) 59-. 



15 



0010 History 

Simson line, historical note on so-called. Muir, 

T. Edinb. Mth. S. P. 3 (1885) 104-. 
" Sinus," origin of word. Ruska, J. Z. Mth. 

Ps. 40 (1895) (H.-lt. Ab.) 126-. 
Sluse, Be'ne' Francois de, geometrician of 17th 

century. Le Paige, C. Ciel et Terre 7 

(188687) 536-, 570-. 
, , letter. Marre, A. Lisb. J. Sc. 

Mth. 10 (1885) 81-. 
Snellius, problem of. Verdam, G. J. Arch. 

Mth. Ps. 2 (1842) 210-. 
Solution of cubic, claims of Cardan and Tar- 

taglia. Zeuthen, H. G. Kjtfb. Ov. (1893) 

303-. 
Sovero, Bartolomeo, mathematician of 17th 

century. Favaro, . Bv. Sc. 33 (1884) 

592. 
Spain, history of mathematics, during 16th 

century. Enestrom, G. Bb. Mth. (1894) 

33-. 
, mathematics in. Galdeano, Z. G. de. Ens. 

Mth. 1 (1899) 6-. 
Spanish writings of 16th and 17th centuries, 

certain. Vicuna, G. Bb. Mth. (1890) 33-. 
Spherical trigonometry formulae, history. Tod- 
hunter, I. Ph. Mg. 45 (1873) 98-. 
, historical sketch. Poreckij, P. S. Kazan 

S. Nt. (Ps.-Mth.) P. 5 (1887) 152-. 
Square root of quadrinomial surd. Bier ens de 

Haan,D. N. Arch. Wisk. 3 (*1877) 208-. 
Steiner (Jakob) and Schlafli (Ludwig), corre- 
spondence between. Graf, J. H. Bern Mt. 

(1896) 61-. 
Stereographic projection, history. Gunther, . 

D. Nf. Tbl. (1887) 227-. 
Stevin, Spinoza and Girard, certain works of. 

Enestrom, G. Stockh. Ofv. (1884) No. 9, 

191- ; Fschr. Mth. (1884) 16-. 
Styrian mathematicians before Kepler. Pein- 

lich, R. Arch. Mth. Ps. 54 (1872) 470-. 
Summation of series of cubes (passages from 

MSS.). Woepcke, F. (vm) A. Mt. 5 (1863) 

147- ; Liouv. J. Mth. 9 (1864) 337-; 10 

(1865) 83-. 
Sweden, history of arithmetic. Hultman, F. W. 

Ts. Mt. Fys. 1 (1868) 1-, 53-, 149-, 245-; 

2 (1869) 57-, 105- ; 3 (1870) 7-, 49-, 241- ; 

4 (1871) 5-, 97-, 209-. 
, mathematical sciences before 1679. 

Dahlin, E. M. Ups. Arsk. (1875) iv + 

146pp. 
, mathematics up to 1600. Enestrom, 

G. Stockh. Ofv. (1889) 489-; Fschr. Mth. 

(1889) 3-. 
, mathematics, Peder Mansson, three small 

treatises. Enestr&m, G. Bb. Mth. (1888) 

Swedenborg, Emanuel, as a mathematician. 

Enestrom, G. [1889] Stockh. Ak. Hndl. 

Bh. 15 (Afd. 1) (1890) No. 12, 29 pp. ; Fschr. 

Mth. (1890) 20. 
Swedenborg's mathematical works. Enestrom, 

G. Stockh. Ofv. (1889) 529-. 
Switzerland, history of mathematics. Wolf, 

R. Bern Mt. (1845) 121-, 137- ; (1846) 

161-, 209- ; (1847) 101-, 129-, 161- ; 1848 

46-, 217-, 269-. 



History 0010 

Switzerland, history of mathematics and 

physics. Wolf, R. Bern Mt. (1847) 68-. 
Symbols, origin. Davis, H. S. Pop. As. 5 

(1898) 402-. 
Symmedian point, early history. Mackay, J. S. 

Edinb. Mth. S. P. 11 (1893) 92-. 
"Ta Yen," so-called rule, in Europe. Curtze, 

M. Z. Mth. Ps. 41 (1896) (H.-lt. Ab.) 81-. 
Talmud, mathematics. Mahler, E. Z. Mth. 

Ps. 31 (1886) (H.-lt. Ab.) 121-. 

as source for mathematical history. Mahler, 
. D. Nf. Tbl. (*1882) 125-. ' 

Taurinus, Franz Adolph. Contribution to the 

previous history of non-Euclidian geometry. 

Stackel, P. Z. Mth. Ps. 44 (1899) (Suppl.) 

399. 
Terminology of the oldest mathematical writings 

in the German language. Mailer, F. Z. 

Mth. Ps. 44 (1899) (Suppl.) 301-. 
Tests for divisibility of numbers (historical). 

Fontes, . Toul. Ac. Sc. Mm. 5 (1893) 

459-. 
"Thabit Ben Korra," Steinschneider, remarks. 

Curtze, M. (vn) [1873] Z. Mth. Ps. 19 

(1874) 95-. 
Theory of numbers in XV. century. Curtze, M. 

Bb. Mth. (1895) 37-. 

, Format's contention with Wallis. 
Wertheim, G. Z. Mth. Ps. 44 (1899) (Suppl.) 
555-. 

, origin and development. Studnicka, 

F. J. Casopis 4 (* 1874) 1-. 
Torricelli and first rectification of a curve. 

Loria, G. Em. E. Ac. Line. Ed. 6 (1897) 

(Sem. 2) 318-. 
. Bordiga, G. Em. E. 

Ac. Line. Ed. 7 (1898) (Sem. 1) 28-. 
Towarzystwo Nauk Scisi'ych (Society of the 

exact sciences) in Paris, 1870-82, origin and 

development. Folkierski, W. Prace Mt.- 

Fiz. 6 (1895) 151- ; Fschr. Mth. (1895) 43. 
" Tractatus de Abaco," end of 12th or beginning 

of 13th century. Curtze, M. Z. Mth. Ps. 

43 (1898) (H.-lt. Ab.) 122-. 
Trapezium, Brahmegupta's. Zeuthen, H. G. 

(xn) Ts. Mth. 6 (1876) 168-, 181- ; 6 (1882) 

97-; 1 (1883) 145-. 

in Euclid, Hero, and Brahmegupta. Weiss- 
enborn, H. Z. Mth. Ps. 24 (1879) (Suppl.) 
167-, 185-. 

Trigonometrical canon , earliest . De Morgan, A . 

As. S. M. Not. 6 (1843-45) 221-. 
Trigonometry in antiquity. Ideler, C. L. Zach 

M. Cor. 26 (1812) 3-. 
. Zeuthen, H. G. Bb. Mth. 1 (1900) 

20-. 
Christian middle ages. Curtze, M. Bb. 

Mth. 1 (1900) 321-. 
, history. Braunmuhl, A. von. Ac. Nt. C. 

N. Acta 71 (1898) 1-. 
Trisection of angle, classification of solutions. 

Baker, M. Smiths. Misc. Col. 33 (1888) 

Art. 4, 96-. (Wash. Ph. S. Bll. 10 (1888).) 
Trochoids, history. Hoza,F. Casopis 1 (* 1872) 

Twilight, problem of the shortest. Zelbr, 
K. Z. Mth. Ps. 41 (1896) (H.-lt. Ab.) 121-, 
153-. 



1C 



0010 Biography 

Tycho Brahe's table of sines. Studnicka, F. J. 

Prag Sb. (1899) (Mth.-Nt.) No. 39, 4 pp. 
Unverzagt's linear coordinates. Eudio, F. 

Z. Mth. Ps. 44 (1899) (Suppl.) 383-. 
Vandermonde, Charles Auguste. Lacepede, 

B. G. E. (le comte de). Par. Mm. de PI. 1 

(1798) (H.) xix-. 
, Christian names. Simon, H. Z. Mth. Ps. 

41 (1896) (H.-lt. Ab.) 83-. 
Viete, Frangois, discoveries. (Quadrature of 

circle, &c.) Bitter, F. As. Fr. C. B. (1879) 

143-. 
, , inventor of modern algebra. Eitter, F. 

As. Fr. C. E. (1892) (Pt. 2) 17-. 
, , new algebra. Eitter, F. As. Fr. C. 

E. (1892) (Pt. 2) 177-. 
_, _, trigonometry. Eitter, F. As. Fr. C. 

E. (1892) (Pt. 2) 208-. 
Wallis's investigation of expression for IT. 

Cayley, A. QJ. Mth. 23 (1889) 165-. 
"Wargentin, P. W., and the so-called Halley 

method in mathematical statistics. Enestrom, 

G. Z. Mth. Ps. 44 (1899) (Suppl.) 81-. 
Weierstrass, his significance for pure mathe- 
matics. Vasiljev, A. V. Kazan S. Nt. (Ps.- 

Mth.) P. 4 (1886) 21-. 
, mathematical work. Poincare, H. Acta 

Mth. 22 (1899) 3-. 
Wronski, mathematical discoveries. Dickstein, 

S. Bb. Mth. (1892) 48-, 85-; (1893) 9-; 

(1894) 49-, 85-; (1896) 5-. 
Ziegler's commentary on " Saphea " of Zarkali. 

Enestrom, G. Bb. Mth. (1896) 53-. 



BIOGEAPHY. 

Abel, Niels Henrik. Mon. Sc. 12 (1870) 660- ; 
Bordeaux S. Sc. Mm. 1 (1884) 368 pp. 

Abria, Jeremie Joseph Benoit. Bordeaux S. 
Sc. Mm. 3 (1893) 301-. 

Adams, John Couch. Am. J. Sc. 43 (1892) 248 ; 
As. J. 11 (1892) 112 ; Educ. Times 45 (1892) 
70-; Eng. S. T. (1892) 251- ; Lpldina. 28 
(1892) 56 ; L. Ps. S. P. 11 (1892) (Ann. Meet.) 
11-; Manch. Lt. Ph. S. Mm. & P. 5 (1892) 
186- ; Nt. 45 (1892) 301- ; Obs. 15 (1892) 
173- ; Am. Ac. P. 27 (1893) 444-; As. S. M. 
Not. 53 (1893) 184-, [348] ; Edinb. E. S. P. 
20 (1895) i-. 

Airy, (Sir) George Biddell. Am. J. Sc. 43 

(1892) 248 ; A. Ps. C. (Berl. Ps. Gs. Vh. 11) 
45 (1892) 601- ; As. J. 11 (1892) 96, 168 ; As. 
Nr. 129 (1892) 33-; As. S. M. Not. 52 (1892) 
212- ; C. E. 114 (1892) 91- ; 115 (1892) 1117- ; 
Eng. S. T. (1892) 244-; I. CE. P. 108 (1892) 
391- ; Lpldina. 28 (1892) 54 ; Manch. Lt. Ph. 
S. Mm. & P. 5 (1892) 185- ; N. S. W. E. 
S. J. 26 (1892) 2- ; Nt. 45 (1892) 232- ; Obs. 
15 (1892) 74- ; E. S. P. 51 (1892) i- ; Science 
19 (1892) 64-; Am. Ac. P. 27 (1893) 446-; 
Edinb. E. S. P. 19 (1893) i- ; Kazan S. Ps.- 
Mth. Bll. 2 (1893) (Prot.) 24-; Met. S. QJ. 
19 (1893) 97. 

Albeggiani, Giuseppe. Palermo Cir. Mt. Ed. 7 

(1893) 39-. 

Alberti, Leon Battista. Bb. Mth. (1895) 9-. 



Biography 0010 

Alvord, (Gen.) Benjamin. Smiths. Misc. Col. 

33 (1888) Art. 2, 127-. (Wash. Ph. S. Bll. 7 

(1885).) 

Ameseder, Adolf. Mh. Mth. Ps. 2 (1891) 479. 
Ampere, Andre Marie. Smiths. Ep. (1872) 

111-; Amiens Ac. Mm. 7 (1881) 261- ; A. 

Tel. 16 (1889) 84-. 
Audouard, Etienne Prosper. Brest S. Ac. Bll. 

20 (1895) 475-. 
August, Friedrich Wilhelm Oscar. Lpldina. 36 

(1900) 46-. 
Avery, Eobert Stanton. Wash. Ph. S. Bll. 12 

(1895) 435-. 
Azzarelli, Mattia. Em. N. Line. At. 51 (1897) 

49-. 
Babbage, Charles. As. S. M. Not. 32 (1872) 

101- ; Devon. As. T. 5 (1872) 30-; Am. Ac. 

P. 8 (1873) 455- ; Smiths. Ep. (1873) 162-. 
Babinet, Jacques. Ev. Cours. Sc. 3 (1872) 409- ; 

Kv. Sc.-Ind. 4 (1872) 294-. 
Bach, . Nancy S. Sc. Bll. (1885) xxxi-. 
Badon-Ghijben, Jacob. Amst. Jb. Ak. (1873) 20-. 
Baehr, George Frederik Willem. Amst. Ak. 

Vs. 7 (1899) 131-. 
Battaglini, Giuseppe. Ven. I. At. (1893-94) 

1419- ; G. Mt. 32 (1894) 205- ; Nap. Ed. 33 

(1894) 49-; Palermo Cir. Mt. Ed. 8 (1894) 

180- ; Em. E. Ac. Line. Mm. 1 (1894) 558-, 

665 ; Ev. Mt. 4 (1894) 91-; Tor. Ac. Sc. At. 

29 (1894) 678-. 

Bauernfeind, Carl Maximilian von. Lpldina. 

30 (1894) 161 ; 31 (1895) 62-, 78-, 94-; Forster 
Al. Bauztg. 60 (1895) 31- ; Munch. Ak. Sb. 
25 (1896) 161-. 

Bellavitis, Giusto. Bll. Sc. Mth. As. 4 (1880) 

343-; Em. E. Ac. Line. T. 5 (1881) 15-; Z. 

Mth. Ps. 26 (1881) (H.-lt. Ab.) 153- ; Ven. 

I. At. 8 (1882) 395- ; Nap. Ac. Pont. At. 15 

1883 (Pt. 1) 5-; Em. S. It. Mm. 6 (1887) 

Ixxiii-. 
Beltrami, Eugenia. Nt. 61 (1899-1900) 568- ; 

Ven. I. At. (1899-1900) (Pt. 1) 72-; A. Mt. 

4 (1900) 151- ; Bologna Ed. 4 (1900) 91- ; C. 

E. 130 (1900) 677- ; 131 (1900) 1037- ; Ens. 

Mth. 2 (1900) 173- ; G. Mt. 38 (1900) 355- ; 

Mil. I. Lomb. Ed. 33 (1900) 241- ; Nap. Ed. 

39 (1900) 74-; Palermo Cir. Mt. Ed. 14 

(1900) 275-; Em. E. Ac. Line. Ed. 9 (1900) 

(Sem. 1) 139- ; Tor. Ac. Sc. At. 35 (1900) 

355- or 541- ; Wiad. Mt. 4 (1900) 266-; 

Kazan S. Ps.-Mth. Bll. 10 (1901) (Prot.) 32-; 

Munch. Ak. Sb. 30 (1901) 345-. 
Berg, Franciscus JoJumnes van den. 's Gravenh. 

I. Ing. Ts. (1891-92) (Verg.) 133; N. Arch. 

Wisk. 1 (1895) 1- ; Amst. Ak. Jb. (1897) 97-. 
Bertrand, Joseph Louis Francois. Nt. 61 (1899- 

1900) 614- ; C. E. 130 (1900) 961- ; 131 

(1900) 1033- ; G. Mt. 38 (1900) 171- ; J. 

Sav. (1900) 257-, 312- ; Lpldina. 36 (1900) 

129- ; Science 11 (1900) 637 ; St Pet. Ac. 

Sc. Bll. 12 (1900) xxxiv ; Wiad. Mt. 4 (1900) 

267-. 
Betti, Enrico. Nap. Ed. 31 (1892) 143-; N. Cim. 

32 (1892) 5- ; Palermo Cir. Mt. Ed. 6 (1892) 

245-; Ev. Mt. 2 (1892) 151- ; A. Mt. 20 

(1892-93) 256 ; Ven. I. At. (1892-93) 609-. 
Biervliet, Albert Marie Joseph van. Brux. S. 

Sc. A. 15 (1891) (Pt. 1) 86. 



0010 Biography 

Bjorling, Emanuel Gabriel. Stockh. Vt. Ak. 

Lefn. 2 (1878-85) 89-. 
Bobek, Karl. Mh. Mth. Ps. 11 (1900) 97-. 
Boltshauser, Giovanni Adamo. Sav. Ac. Mm. 

6 (1897) Ixxxiii-. 
Bolyai de Bolya, Johann. Bordeaux Mm. S. 

Sc. 5 (1867) 203- ; Z. Mth. Ps. 42 (1897) 

(Suppl.) 133-. 
Bolyai de Bolya, (Farkas) Wolfgang. Bordeaux 

Mm. S. Sc. 5 (1867) 192- ; Mag. Tud. Ak. 

Etk. (Mth.) 11 (1885) No. 9, 36 pp. 
Bolzani, Josef For tunatus. Kazan Un. Bll. 12 

(1876) 208-. 
Boncompagni, (il principe) Baldassarre. Em. 

N. Line. At. 47 (1894) 161- ; Z. Mth. Ps. 39 

(1894) (H.-lt. Ab.) 201-. 
Bonnaire, Antoine Francois Donat. Caen Ac. 

Mm. (1891) (Ft. 2) 95, 95-. 
Bonnet, Pierre Ossian. C. E. 115 (1892) 

1115-; 117 (1893) 1014- ; Lpldina. 28 (1892) 

Boole,' George. E. S. P. 15 (1867) vi-; Leic. 

S. T. (1835-79) 272-. 
Booth, (Rev.) James. Educ. Times 31 (1878) 

126-. 

Boschi, Pietro. Bologna Ed. (1887-88) 10-. 
Bouquet, Jean Claude. Bll. Sc. Mth. 9 (1885) 

301- ; C. E. 101 (1885) 585-; 102 (1886) 

1267- ; N. Antol. Sc. 83 (1885) 404. 
Bour, Jacques Edmond Emile. Par. S. Phlm. 

Bll. 3 (1866) 119- ; N. A. Mth. 6 (1867) 145- ; 

Eec. Mth. (Moscou) 2 (1867) (Pt. 2) 44-. 
Brassai, Samuel. Mag. Tud. Ak. Ets. 10 

(1899) 276-. 
Brassinne, Philippe Emile. Toul. Ac. Sc. Mm. 

7 (Sem. 2) (1885) 25-. 
Bravais, Auguste. Par. Ac. Sc. Mm. 35 (1866) 

xxiii-; Smiths. Ep. (1869) 145-. 
Breton, Philippe. Isere S. Bll. 27 (1892) 391-. 
Bretschneider, Carl Anton. Z. Mth. Ps. 24 

(1879) (H.-lt. Ab.) 73-. 
Brianchon, Charles Julien. Ev. Sc. 1 (1894) 

592-. 
Brioschi, Francesco. A. Mt. 26 (1897) 343-; 

C. E. 125 (1897) 1139- ; Em. E. Ac. Line. 

Ed. 6 (1897) (Sem. 2) 353- ; Nt. 57 (1897-98) 

279 ; Crelle J. Mth. 119 (1898) 259 ; G. Mt. 

36 (1898) 51- ; L. Mth. S. P. 29 (1898) 721- ; 

Manch. Lt. Ph. S. Mm. & P. 42 (1898) 

xxxix ; Mth. A. 50 (1898) 477- ; N. Antol. 

Sc. 157 (1898) 170- ; Nap. Ed. 37 (1898) 3- ; 

Ev. Sc.-Ind. 30 (1898) 28 ; St. P<*t. Ac. Sc. 

Bll. 8 (1898) xxvii-; Wiad. Mt. 2 (1898) 66-; 

Wien. Aim. 48 (1898) 332- ; Mil. I. Lomb. 

Ed. 32 (1899) 108- ; Miinch. Ak. Sb. 28 

(1899) 449-; Mathesis 20 (1900) 112- ; 

Palermo Cir. Mt. Ed. 14 (1900) 262-. 
Brisse, Charles Michel. 3. de Ps. 7 (1898) 

[637] ; Nt. 59 (1898-99) 80 ; N. Y. Am. Mth. 

S. Bll. 5 (1899) 211-. 
Broch, Ole Jacob. Christiania F. (1889) (Ov.) 

12-; Nt. 39 (1889) 375 ; Ev. Sc. 43 (1889) 218. 
Bubendey, Georg Heinrich (sen.). Lpldina. 

25 (1889) 215. 

Buchheim, Arthur. Nt. 38 (1888) 515-. 
Buka, Felix. Lpldina. 33 (1897) 49 ; D. Mth. 

Vr. Jbr. 6 (1899) (Heft 1) 23-. 



Biography 0010 

Bumakovskij , Viktor Jakovlevic. Lpldina. 25 

(1889) 219 ; Fschr. Mth. (1890) 30 ; Kharkov 
Mth. S. Com. 2 (1891) 149-. 

Buys-Ballot, Christoph Heinrich Diederich. 
Brux. Ac. Bll. 19 (1890) 180- ; Lpldina. 26 

(1890) 58 ; Manch. Lt. Ph. S. Mm. & P. 3 
(1890) 167- ; Nt. 41 (1890) 371 ; Met. S. QJ. 

17 (1891) 61-; Met. Z. 8 (1891) 1-; Sym. 
Met. Mg. 25 (1891) 8 ; Amst. Ak. Jb. (1899) 
59-. 

Casey, John. L. Mth. S. P. 22 (1891) 477-; 

Lpldina. 27 (1891) 155 ; Mathesis 11 (1891) 

13 ; E. S. P. 49 (1891) xxiv-. 
Casorati, Felice. Bb. Mth. (1891) 1- ; Lpldina. 

27 (1891) 52 ; Palermo Cir. Mt. Ed. 5 (1891) 

236- ; Mil. I. Lomb. Ed. 25 (1892) 1206-. 
Catalan, Eugene Charles. Nt. 49 (1893-94) 437 ; 

Brux. Ac. Bll. 27 (1894) 326-, 330- ; Lpldina. 

30 (1894) 112 ; Mathesis 14 (1894) 33 ; Kazan 

S. Ps.-Mth. Bll. 4 (1895) (Prot.) 84. 
, , letters to some mathematicians. 

Liege S. Sc. Mm. 17 (1892) No. 5, 22 pp. ; 

18 (1895) No. 5, 36 pp. 

, , mathematical work. Liege S. Sc. 

Mm. 12 (1885) No. 1, 38 pp. 
Cauchy, (le baron) Augustin Louis. J. Sav. 

(1869) 205- ; Ev. Sc. 9 (1898) 97-. 
Cayley, Arthur. J. H. Un. Cir. [14 (1894-95)] 

51 ; Nt. 51 (1894-95) 323 ; Bll. Sc. Mth. 19 

(1895) 189- ; C. E. 120 (1895) 233- ; Crelle 

J. Mth. 115 (1895) 349- ; L. Mth. S. P. 26 

(1895) 546- ; Manch. Lt. Ph. S. Mm. & P. 

9 (1895) 235- ; Mth. A. 46 (1895) 462- ; N. Y. 

Am. Mth. S. Bll. 1 (1895) 133- ; Obs. 18 

(1895) 112- ; Em. E. Ac. Line. Ed. 4, 1895 

(Sem. 1) 177- ; E. S. P. 58 (1895) i-; Ev. Sc. 

3 (1895) 188; As. S. M. Not. 56 (1896) 191- ; 
. Kazan S. Ps.-Mth. Bll. 5 (1896) (Prot.) 29-. 
Cebysev (Tchebichef), Pafnutij Lvovic. C. E. 

119 (1894) 1048- ; Kharkov Mth. S. Com. 4 

(1895) 263- ; Lpldina. 31 (1895) 55 ; Nt. 52 
1895 345 ; Science 1 (1895) 129- ; St Pet. 

Ac. Sc. Bll. 2 (1895) x-, 189- ; Fschr. Mth. 

(1899) 15- ; Mathesis 20 (1900) 67-. 
Cellerier, Charles. Gen. S. Ps. Mm. 31 (1890- 

93) xviii-. 
Challis, James. As. S. M. Not. 43 (1883) 160- ; 

Obs. 6 (1883) 23. 
Charles, Jacques Alexandre Cesar. Par. Mm. 

Ac. Sc. 8 (1829) (H.) 73-. 
Chasles, Michel. Bologna Ed. (1881) 37-; E. 

S. P. 32 (1881) i- ; Kharkov Mth. S. Com. 

(1881) 23-; Kosmos (Lw.) 6 (1881) 555-; 

Ev. Sc. 50 (1892) 801-. 
Chelini, Domenico. Bll. Sc. Mth. As. 3 (1879) 

228-; Em. N. Line. At. 32 (1879) 152- ; Em. 

E. Ac. Line. T. 3 (1879) 54-; Em. S. It. 

Mm. 6 (1887) Iviii-. 
Chio, Felice. Ev. Sc.-Ind. 3 (1872) 61. 
Clebsch, Rudolf Friedrich Alfred. Gott. Nr. 

(1872) 550- ; Mil. I. Lomb. Ed. 5 (1872) 
1041- ; Ts. Mth. 2 (1872) 190- ; G. Mt. 11 

(1873) 44- ; 12 (1874) 29- ; Mth. A. 6 (1873) 
197- ; 7 (1874) 1-; A. Mt. 6 (1875) 153-. 

Close, (Maj.-Gen.) Frederick. L. Mth. S. P. 

31 (1900) 488-. 
Coaldey, George W. Am. J. Sc. 46 (1893) 484 ; 

Lpldina. 29 (1893) 204 ; Nt. 48 (1893) 398. 



18 



0010 Biography 

Cockle, (Sir) James. As. S. M. Not. 55 (1895) 

192 ; L. Mth. S. P. 26 (1895) 551- ; Manch. 

Lt. Ph. S. Mm. & P. 9 (1895) 215- ; R. S. P. 

59 (1896) xxx-. 
Coffin, John Hunting ton Crane. Am. Ac. P. 

25 (1890) 312- ; Am. J. Sc. 39 (1890) 246. 
Correnti, Cesare. Firenze Ac. Georg. At. 11 

(1888) xxxix-. 
Cotterill, Thomas. L. Mth. S. P. 12 (1880-81) 

217-. 
Craig, Thomas. J. H. Un. Cir. [19 (1899- 

1900)] 67. 
Dalgas, Gustavo. Firenze Ac. Georg. At. 11 

(1888) xxxv-. 

Dauge, Felix. Mathesis 19 (1899) 177-. 
David, Claude Alexandre. Lille S. Mm. 1 

(1865) 452-. 
David, Jean Marie. Toul. Ac. Sc. Mm. 2 (1890) 

528-. 
Davidov, Avgust Julievic. Rec. Mth. (Moscou) 

15 [1891] 1-; Fschr. Mth. (1890) 29. 
Davies, Griffith. Assur. Mg. 5 (1855) 337-. 
Decrue, David. Sch. Nf. Gs. Vh. (1892) 208-. 
De la Gournerie, Jules Antoine Rene Maillard. 

Par. Ac. Sc. Mm. 44 (1888) cxxxvii-; A. 

Cons. Arts et Met. 8 (1896) 23-. 
Delsaulx, (le rev. pere) Joseph. Brux. S. Sc. 

A. 15 (1891) (Ft. 1) 86-. 
De Morgan, Augustus. Ts. Mth. 1 (1871) 94- ; 

As. . M. Not. 32 (1872) 112-. 
Despeyrous, Theodore. Toul. Ac. Sc. Mm. 7 

(Sem. 2) (1885) 100-. 

Dienger, Josef. Crelle J. Mth. 115 (1895) 350. 
Dodgson, (Rev.) Charles Lutwidge (Pseudonym: 

Lewis Carroll). Nt. 57 (1897-98) 279-, 303 ; 

N. Y. Am. Mth. S. Bll. 4 (1898) 241. 
Dodson, James. I. Act. J. 14 (1869) 341-. 
Drechsler, Hermann Adolf. Dresden Isis Sb. 

(1888) 43 ; Lpldina. 24 (1888) 171 ; 26 (1890) 
193-. 

Drobisch, Moritz Wilhelm. Leip. Mth. Ps. B. 

48 (1896) 697-. 

Du Bois-Reymond, Paul. Crelle J. Mth. 104 

(1889) 352- ; Lpldina. 25 (1889) 112 ; Mth. 
A. 35 (1890) 457- ; Munch. Ak. Sb. 20 (1891) 
415. 

Duhamel, Jean Marie Constant. Ts. Mth. 2 

(1872) 143-. 
Dupin, (le baron) Pierre Charles Francois. 

A. Cons. Arts et Met. 10 (1873) 233-; Ts. 

Mth. 3 (1873) 64; Par. Ac. Sc. Mm. 44 

(1888) i-. 
Durege, Heinrich. Lpldina. 29 (1893) 110; 

Wien Aim. 43 (1893) 264-. 
Eisenstein, Gotthold. Z. Mth. Ps. 40 (1895) 

(Suppl.) 143-. 
Elliott, Ezekiel Brown. Science 11 (1888) 261 ; 

Wash. Ph. S. Bll. 11 (1892) 470-. 
Ellis (Sharpe), Alexander John. L. Mth. S. P. 

21 (1891) 457- ; Nt. 43 (1891) 20 ; R. S. P. 

49 (1891) i-. 

Euler, Leonhard. Basel Vh. 7 (1885) (Anhang) 
39- ; Barcel. Ac. Mm. 1 (1892-1900) 241-. 

Fambri, Paulo. N. Antol. Sc. 153 (1897) 131-. 

Fedorenko, Ivan. As. Nr. 120 (1889) 319- ; 
Lpldina. 25 (1889) 52. 

Ferroni, Pietro. Firenze Ac. Georg. At. 7 
(1830) 33-. 



Biography 0010 

Fink, Karl. Lpldina. 24 (1888) 58 ; D. Mth. 

Vr. Jbr. 7 (1899) (Heft 1) 33-. 
Finlaison, John. Assur. Mg. 10 (1863) 147-. 
Fleck, (I'abbe) Joseph Martin. Metz Ac. Mm. 

79 (1900) 193-. 
Fowler, (Sir) Robert Nicholas. L. Mth. S. P. 

22 (1891) 476-. 

Frost, (Rev.) Percival. L. Mth. S. P. 29 

(1898) 726-; Nt. 58 (1898) 131; N. Y. Am. 

Mth. S. Bll. 4 (1898) 557 ; Science 7 (1898) 

858; R. S. P. 64 (1899) vii-. 
Gabba, Alberto. Brescia At. Cm. (1876) 100-. 
Gabelli, Pasquale. Yen. Aten. 1 (1886) 72-, 

209-. 
Gadolin, Axel Wilhelm. Nt. 47 (1892-93) 232 ; 

Helsingf. Acta 19 (1893) No. 18, 24 pp. 
Galois, Evariste. Par. EC. Norm. A. 13 (1896) 

197-. 
Gascheau, Gabriel. Toul. Ac. Sc. Mm. 6 

(Sem. 2) (1884) 17-. 
Gasco, Luis Gonzaga. Bb. Mth. 1 (1900) 225- ; 

D. Mth. Vr. Jbr. 8 (1900) (Heft 1) 26-. 
Gaskin, (Rev.) Thomas. As. S. M. Not. 48 

(1888) 161- ; R. S. P. 46 (1890) i-. 
Gasparis, Annibale de. Acireale Ac. At. 3 

(1891) viii; As. Nr. 129 (1892) 247-; Nap. 
Ac. Pont. At. 22 (1892) (Append.) 37-; 28 
(1898) No. 1, 7 pp. ; Nap. I. Inc. At. 5 (1892) 
9; Nap. Rd. 31 (1892) 65-; Nt. 45 (1892) 
612; Obs. 15 (1892) 231- ; As. S. M. Not. 53 
(1893) 225-. 

Gauss, Johann Friedrich Karl. R. S. P. 7 

(1856) 589-; Casopis 6 (1877) 145- ; Nt. 15 

(1877) 533-; 28 (1883) 272-; Science 9 (1899) 

697-. 
Genocchi, Angelus Joannes Bartholomaeus 

Aloysius. Nap. Rd. 28 (1889) 79; Tor. Ac. 

Sc. Mm. 39 (1889) 463-. 
Gergonne, Joseph Diez. Mntp. Mm. Ac. Sect. 

Md. 3 (1862) 191-. 
Gerhardt, Karl Immanuel. Lpldina. 35 (1899) 

136; Bb. Mth. 1 (1900) 205- ; D. Mth. Vr. 

Jbr. 8 (1900) (Heft 1) 28-. 
Germain, (Mile.) Sophie. Ausl. 5 (1832) 623-. 
Gibbes, Lewis R. Am. J. Sc. 49 (1895) 80. 
Gierster, Josef. D. Mth. Vr. Jbr. 2 (1893) 44-. 
Gilbert, Louis Philippe. Brux. S. Sc. A. 16 

(1892) (Pt. 1) 102- ; Mathesis 12 (1892) 57; 
Par. S. Phlm. Bll. 4 (1892) 138-. 

Gill, Charles. Assur. Mg. 6 (1857) 216-. 
Giorgini, Gaetano. G. Mt. 31 (1893) 23-. 
Gogu, Constantin. Bucarest S. Sc. Bll. (1897) 

103-, 109-. 
Gompertz, Benjamin. As. S. M. Not. 26 (1866) 

104- ; Assur. Mg. 13 (1867) 1-. 
Graindorge, Joseph. Mathesis 16 (1896) 48. 
Grassmann, Hermann Gunther. Z. Mth. Ps. 

23 (1878) (H.-lt. Ab.) 69-; Mth. A. 14 (1879) 

Graves, (Rt. Rev.) Charles. Nt. 60 (1899) 277. 
Graves, John Thomas. R. S. P. 19 (1871) 

xxvii . 
Gray, Peter. I. Act. J. 26 (1887) 301- ; As. S. 

M. Not. 48 (1888) 163-. 
Gretschel, Heinrich Friedrich. Lpldina. 28 

(1892) 57; D. Mth. Vr. Jbr. 2 (1893) 42-. 
Grofe, Gustav von. Dorpat Sb. 11 (1896) 186-. 

19 B2 



0010 Biography 

Gromeka, Ippollt Stepanovic. Kazan S. Nt. 
(P*. Mth.) P. 8 (1890) 163 (bis)-, 168-, 181- ; 
Fschr. Mth. (1890) 30. 
Gronau, Johann Friedrich Wilhelm. Danzig 

Schr. 7 (Heft 1) (1888) i-. 
Grunert, Johann August. Arch. Mth. Ps. 55 

(1873) 1-; Wien Aim. (1873) 145-. 
Gunther, Paul. D. Mth. Vr. Jbr. 1 (1892) 10 ; 

Z. Mth. Ps. 37 (1892) (H.-lt. Ab.) 46-. 
Guthrie, Francis. J. Bt. 37 (1899) 528; Nt. 61 

(1899-1900) 84. 

Gylde"n, Johann August Hugo. C. B. 123 (1896) 
771- ; Lpldina. 32 (1896) 189; Obs. 19 (1896) 
446; Nt. 55 (1896-97) 38, 158- ; Acta Mth. 
20 (1897) 397-; As. Nr. 142 (1897) 49-; As. 
S. M. Not. 57 (1897) 222-; Bll. As. 14 
(1897) 289-; Wiad. Mt. 1 (1897) 31-. 
Hachette, Jean Nicolas Pierre. Fr. S. Ag. Mm. 

(1834) 143-. 
Hallauer, Octave Rene. Mulhouse S. In. Bll. 

54 (1884) 139- ; Science 4 (1884) 306-. 
Halphen, Georges Henri. C. E. 109 (1889) 
994-; 110 (1890) 489-; Liouv. J. Mth. 5 
(1889) 345-; Palermo Cir. Mt. Ed. 3 (1889) 
210- ; Em. E. Ac. Line. Ed. 5 (1889) (Sem. 
1) 815- ; J. H. Un. Cir. [9 (1889-90)] 26; 
Bll. Sc. Mth. 14 (1890) 62-; Par. EC. Pol. J. 
60 (1890) 137-. 

Hamilton, (Sir) William Rowan. Am. J. Sc. 
42 (1866) 293-; As. S. M. Not. 26 (1866) 
109- ; Ir. Ac. P. 9 (1867) 307-. 
Hankel, Hermann. Mth. A. 7 (1874) 583-. 
Hargreave, Charles James. E. S. P. 16 (1868) 

xvii-. 

Harnack, Carl Gustav Axel. Dresden Isis Sb. 
(1888) (Ab.) 3-; Lpldina. 24 (1888) 110- ; 
Mth. A. 32 (1888) 161- ; Z. Mth. Ps. 33 
(1888) (H.-lt. Ab.) 121-. 
Haughton, (Rev.) Samuel. Gl. Mg. 4 (1897) 
573-; I. ME. P. (1897) 514-; Nt. 57 (1897- 
98) 55-; Gl. S. QJ. 54 (1898) Ixvi-; E. S. P. 
62 (1898) xxix-. 
Haydon, Frank Scott. L. Mth. S. P. 18 (1886- 

87) 392. 
Heilermann, Hermann. Z. Mth. Ps. 45 (1900) 



(H.-lt. Ab.) 57. 
iellwig, Karl ~ 



Hellwig, Karl Franz. Erfurt Ak. Jb. 24 (1898) 

292. 
Heppel, George Hastings. Assur. Mg. 10 (1863) 

83. 
Hermite, Charles. Manch. Lt. Ph. S. Mm & 

P. 45 (1901) xxxviii-. 
Herr, Josef Philipp. Lpldina. 20 (1884) 221- ; 

As. Nr. Ill (1885) 79-. 
Herschel, (Sir) John F. W. Brux. Ac. Bll. 31 

(1871) 478-; Smiths. Ep. (1871) 109- ; Am. 
Ph. S. P. 12 (1872) 217- ; As. S. M. Not. 32 

(1872) 122- ; Edinb. E. S. P. 7 (1872) 543-; 
E. S. P. 20 (1872) xvii-; Am. Ac. P. 8 (1873) 
461- ; Wien Aim. (1873) 147-. 

Hesse, Ludwig Otto. Ts. Mth. 4 (1874) 190- ; 

Crelle J. Mth. 79 (1875) 345-. 
Hilgard, Julius Erasmus. Am. Ac. P 26 

(1891) 370- ; Am. J. Sc. 41 (1891) 526; 

Lpldina. 27 (1891) 108; Nt. 44 (1891) 87; 

Eailroad & Eng. J. 65 (1891) 283-; Science 

17 (1891) 272; Wash. Ph. S. Bll. 12 (1895) 

462. 



Biography 0010 

Hill, Thomas. Am. Ac. P. 27 (1893) 426-. 
Hirst, Thomas Archer. Lpldina. 28 (1892) 59 ; 

Nt. 45 (1892) 399-; As. S. M. Not. 53 (1893 

218- ; E. S. P. 52 (1893) xii-; L. Ps. S. P. 

12 (1894) (Ann. Meet. 1893) 9. 
Hochheim, Karl Adolf. Lpldina. 34 (1898) 

130. 
Holmgren, Hjalmar Josef. Acta Mth. 7 (1885) 

392. 

Romans, Sheppard. I. Act. J. 34 (1899) 144-. 
Hopkinson, John. Elektech. Z. 19 (1898) 617 ; 

I. ME. P. (1898) 534-; L. Mth. S. P. 29 

(1898) 727-; Nt. 58 (1898) 419- ; I. CE. P. 

135 (1899) 338-; L. Ps. S. P. 16 (1899) (Ann. 

Meet.) 9 ; E. S. P. 64 (1899) xvii-. 
Hoppe, Ernst Reinhold Eduard. Lpldina. 36 

(1900) 132. 
Homer, Johann Caspar. Ziir. Vischr. 41 

(1896) (Festschr. Th. 1) 79-. 
Horner, Johann Jakob. Ziir. Vjschr. 41 (1896) 

(Festschr. Th. 1) 227-. 
Hoiiel, Guillaume Jules. Lpldina. 22 (1886) 

167- ; Bordeaux S. Sc. Mm. 4 (1888) 1-. 
Hunyady, Jend. Mag. Tud. Ak. Ets. 2 (1891) 

Imseneckij, Vasllij Grigorjevic. Kazan S. Ps.- 

Mth. Bll. 2 (1893) (Prot.) 15-; 3 (1893) 37-; 

Eec. Mth. (Moscou) 18 1896) 347-; Fschr. 

Mth. (1896) 19. 
Isbister, Alexander Kennedy. Educ. Times 36 

(1883) 189- ; Peterm. Mt. 30 (1884) 101-. 
Jacobi, Carl Gustav Jacob. Grunert Arch. 22 

(1853) 158-. 
Janni, Vincenzo. Nap. Ac. Pont. At. 22 (1892) 

(App.) 83-. 
Jeffery, Henry Martyn. Cornwall Pol. S. Ep. 

(1891) 16-; L. Mth. S. P. 22 (1891) 479-; 

E. S. P. 50 (1892) vii-; Cornwall E. I. J. 11 

(1895) 208-. 
Jellett, (Rev.) John Hewitt. Nt. 37 (1888) 

396. 

Jellicoe, diaries. I. Act. J. 24 (1884) 17-. 
Kelland, Philip. E. S. P. 29 (1879) vii-; 

Edinb. E. S. P. 10 (1880) 321-. 
Kendall, E. Otis. Nt. 59 (1898-99) 300; N. Y. 

Am. Mth. S. Bll. 5 (1899) 272. 
Kieseritzky, Johann Georg Gustav. Lpldina. 

32 (1896) 180-. 
Kirchhoff, Gustav Robert. A. di C. 6 (1887) 

380; Am. J. Sc. 34 (1887) 496; Berl. B. 20 

(1887) 2771- ; Elektech. Z. 8 (1887) 457-; 

Lpldina. 23 (1887) 216; Nt. 36 (1887) 606- ; 

Obs. 10 (1887) 396; Tor. Ac. Sc. At. 23 

(1887-88) 2-; Am. Ac. P. 23 (1888) 370- ; 

As. Nr. 118 (1888) 47-; A. Tel. 15 (1888) 

96; L. Ps. S. P. 9 (1888) (Ann. Meet.) 12-; 

Phm. J. 18 (1888) 376; Wien Aim. 38 (1888) 

193-; Gott. Ab. 35 (1889) (Mth.) 10 pp.; 

Smiths. Ep. (1889) 527-; E. S. P. 46 (1890) 

vi . 
Kirkman, (Rev.) Thomas Penyngton. Manch. 

Lt. Ph. S. Mm. & P. 9 (1895) 238-. 
Klein, Benno. D. Mth. Vr. Jhr. 1 (1892) 9. 
Koch, JoJiann Rudolf. Bern. Mt. (1891) xxii-. 
Kornuch-Trockij, Jakov Petrovic. As. Nr. 145 

(1898) 127- ; Kazan S. Ps.-Mth. Bll. 7 (1898) 

(Prot.) 115-. 
Kossak, Ernst. Lpldina. 28 (1892) 56. 



20 



0010 Biography 



Kotelmikov, Petr Ivanovic. Kazan S. Nt. (Ps.- 
Mth.) P. 5 (1887) 225-; Fschr. Mth. (1887) 
20. 

Kovalevskij, Sofja Vasiljevna. Bll. Se. Mth. 
15 (1891) 212- ; Christiania F. (1891) (Ov.) 
8-; Crelle J. Mth. 108 (1891) 88; Lpldina. 

27 (1891) 59-; Nt. 43 (1891) 375-; Palermo 
Cir. Mt. Ed. 5 (1891) 121- ; Ev. Mt. 1 (1891) 
21-; A. Mt. 19 (1891-92) 201- ; As. & Asps. 
11 (1892) 281- ; Acta Mth. 16 (1892-93) 

'385-; Eec. Mth. (Moscou) 16 (1893) 1-. 
Kraus, Ludwig. Casopis 15 (1886) 49-; Fschr. 

Mth. (1886) 22. 
Kronecker, Leopold. Lpldina. 27 (1891) 207; 

28 (1892) 94-; A. Ps. C. (Berl. Ps. Gs. Vh. 
11) 45 (1892) 595-; C. E. 114 (1892) 19-; 
Mathesis 12 (1892) 18; N. Y. Mth. S. Bll. 1 
(1892) 173- ; Berl. Ak. Ab. (1893) 22 pp. ; D. 
Mth. Vr. Jbr. 2 (1893) 5-; Mth. A. 43 (1893) 
1-; Munch. Ak. Sb. 22 (1893) 202. 

Kummell, diaries Hugo. Wash. Ph. S. Bll. 

13 (1900) 404-. 
Kummer, Ernst Eduard. C. E. 116 (1893) 

1163- ; Lpldina. 29 (1893) 110; D. Mth. Vr. 

Jbr. 3 (1894) 13-; Mathesis 14 (1894) 40-; 

Munch. Ak. Sb. 24 (1895) 140-. 
Kunze, Karl Ludwig Albrecht. Lpldina. 27 

(1891) 78-, 94-. 

Laborie, Edmond. Angers S. Sc. Bll. (1891) 

236. 
Lagrange, Joseph Louis (comte) de. Par. Mm. 

del'I. (1812) (H.) xxvii-; Ts. Mth. 1 (1877) 

129-. 
Laguerre, Edmond Nicolas. C. E. 103 (1886) 

424-; 104 (1887) 1643- ; Par. EC. Pol. J. 56 

(1886) 213- ; N. A. Mth. 6 (1887) 105- ; 7 

(1888) 352. 
Lalanne, Leon Louis Chretien. C. E. 114 

(1892) 569-; 115 (1892) 1118-. 
Lamarle, Anatole Henri Ernest. Brux. Ac. Bll. 

39 (1875) 360-. 
Lame, Gabriel. A. Mines 1 (1872) 271- ; Ev. 

Sc. 14 (1878) 720-. 
Langren, Michel-Florent van. Ciel et Terre 12 

(1891-92) 241-, 297-. 
Laplace, Pierre Simon (le marquis) de. Hall 

Bij. 2 (1826) 284-; Par. Mm. Ac. Sc. 10 

(1831) (H.) 81-. 
Lavagna, Giovanni Maria. Ev. Sc.-Ind. 2 

(1871) 40-. 
Le Besgue, Victor Amedee. N. A. Mth. 16 

(1877) 116-. 
Lefavour, Edward Brown. Wash. Ph. S. Bll. 

11 (1892) 488-. 
Legendre, Adrien Marie. Smiths. Ep. (1867) 

137. 
Lejeune Dirichlet, Gustave Pierre. Tortolini 

A. 3 (1860) 221-, 283-. 

Letnikov, Aleksej Vasiljevic. Eec. Mth. (Mos- 
cou) 14 (1890) i-; Fschr. Mth. (1889) 21. 
Liagre, Jean Baptiste Joseph. Ciel et Terre 11 

(1890-91) 541- ; Brux. Ac. Bll. 21 (1891) 77-. 
Lie, Marius Sophus. Tor. Ac. Sc. At. 34 (1898) 

235- or 363-; Nt. 59 (1898-99) 445-; Arch. 

Mth. Ntvd. 21 (1899) No. 1, xxiii pp.; C. E. 

128 (1899) 525-; 129 (1899) 1062; D. Nf. Vh. 

(1899) (Th. 2, Halfte 1) 4-; Ens. Mth. 1 



Biography 0010 

899) 156; Leip. Mth. Ps. B. 51 (1899) xi-; 
Mth. S. P. 30 (1899) 334-; Lpldina. 35 

(1899) 60; N. Ts. Mth. 10 (B) (1899) 48; 
N. Y. Am. Mth. S. Bll. 5 (1899) 367-; 
Em. E. Ac. Line. Ed. 8 (1899) (Sem. 1) 
281-, 360- ; Science 9 (1899) 447-; St. Pet. 
Ac. Sc. Bll. 10 (1899) xxxiii-; Bb. Mth. 1 

(1900) 166- ; D. Mth. Vr. Jbr. 8 (1900) (Heft 
1) 30-; Kazan S. Ps.-Mth. Bll. 9 (1900) 
(App.) 32 pp.; Manch. Lt. Ph. S. Mm. & P. 
43 (1900) xxxiii-; Mathesis 20 (1900) 228-; 
Mth. A. 53 (1900) 1-; Munch. Ak. Sb. 30 

(1901) 339-. 

Ligin, W. N. Fschr. Mth. (1900) 29. 

Ligowski, Wilhelm. D. Mth. Vr. Jbr. 4 (1897) 
46. 

Liouville, Joseph. Edinb. E. S. P. 14 (1888) 
83 (bis)-. 

Lobacevskij , Nikolaj Ivanovic. Kazan Un. Mm. 
(1857) (Bk. 4) 153- ; Bll. Sc. Mth. As. 1 
(1870) 66-, 324-, 384-; Mathesis 13 (1893) 
117-, 193; Ev. Sc. 52 (1893) 636-; Kazan S. 
Ps.-Mth. Bll. 3 (1893) (Prot.) 27-; 4 (1895) 
(Prot.) 4-; Eec. Mth. (Moscou) 17 (1895) 
474-; Z. Mth. Ps. 40 (1895) (Suppl.) 205- ; 
Bordeaux S. Sc. Mm. 1 (1896) 307-. 

Lobatto, Rehuel. Amst. Jb. Ak. (1866) 25-; 
Arch. Mth. Ps. 49 (1869) 332-. 

Lommel, Eugen Cornelius Joseph von. Elek- 
tech. Z. 20 (1899) 458; Lpldina. 35 (1899) 
160- ; D. Mth. Vr. Jbr. 8 (1900) (Heft 1) 47-. 

Loomis, Elias. Lpldina. 25 (1889) 214; Met. 
Z. 6 (1889) 466-; Nt. 40 (1889) 401; Obs. 12 

(1889) 358; Eailroad & Eng. J. 63 (1889) 
435; Am. Ac. P. 25 (1890) 324-; Am. J. Sc. 
39 (1890) 427-; Met. S. QJ. 16 (1890) 101; 
Sid. Mess. 9 (1890) 241- ; Smiths. Ep. 

(1890) 741- ; Sym. Met. Mg. 24 (1890) 122. 
Lovering, Joseph. Am. J. Sc. 43 (1892) 167; 

Lpldina. 28 (1892) 102; Am. Ac. P. 27 (1893) 

372-. 
Lubbock, (Sir) John William. As. S. M. Not. 

26 (1866) 118- ; E. S. P. 15 (1867) xxxii-. 
Luca, Ferdinando de. II Polit. 18 (1870) 612-. 
Lucas, Edouard. Mathesis 11 (1891) 217. 
Luther, Eduard. Lpldina. 23 (1887) 216; 24 

(1888) 52; Obs. 10 (1887) 432-; As. Nr. 118 

(1888) 31-; As. S. M. Not. 48 (1888) 169- ; 

Kimigsb. Schr. 28 (1888) (Ab.) 105-. 
Lutter, Ndndor (Ferdinand). Lpldina. 28 

(1892) 53; Mag. Tud. Ak. Ets. 3 (1892) 
531-. 

Luvini, Giovanni. Acireale Ac. At. 3 (1891) 

vii. 

M'Cann, H. W. Beng. As. S. P. (1884) 113-. 
Machovec, Franz. Mh. Mth. Ps. 3 (1892) 

403. 
Maddem, Lorenzo. Acireale Ac. At. 2 (1891) 

xv. 
Mainardi, Gaspare. Em. E. Ac. Line. T. 3 

(1879) 126-. 

Majer, Jozef. Wiad. Mt. 3 (1899) 302-. 
Makeham, William Matthew. I. Act. J. 30 

(1893) 1-. 

Maksimovic, Vladimir Pavlovic. Kazan S. Nt. 
(Ps.-Mth.) P. 8 (1890) 53- ; Fschr. Mth. (1890) 



21 



0010 Biography 

Malmsten, Carl Jolian. Acta Mth. 7 (1885) 

394; Goteb. Hndl. 26 (1891) 67-. 
Marsilly, (le gen.) Louis Joseph Auguste de 

Commines de. Bone Ac. Hip. Bll. 24 (1891) 

(C. E. 1890) 1-. 
Masdea, Giuliano. Nap. I. Inc. At. 1 (1899) 

20. 
Mathieu, Emile Leonard. Lpldina. 26 (1890) 

215; Nancy S. Sc. Bll. (1891) 1-; N. Y. 

Mth. S. Bll. 1 (1892) 156-, 236. 
Matthes, Corel Johannes. Amst. Ak. Jb. (1882) 

1-. 

Maus, Henri. Brux. Ac. Bll. 26 (1893) 173-. 
Maxwell, James Clerk. Edinb. K. S. P. 10 

(1880) 331- ; Kosmos (Lw.) 6 (1881) 129- ; 

E. S. P. 33 (1882) i-. 
Mayr, Alois. Lpldina. 26 (1890) 217. 
Mehler, Gustav Ferdinand. Lpldina. 31 (1895) 

170; Mth. A. 48 (1897) 603-. 
Meissel, Ernst Daniel Friedrich. As. Nr. 137 

(1895) 239-; Lpldina. 31 (1895) 102. 
Melinikov, Michail Ivanovic. Kazan S. Nt. 

(Ps.-Mth.) P. 4 (1886) 49-. 
Merrifield, Charles Watkins. L. Ps. S. P. 5 

(1884) (Ann. Meet.) 13-; Nt. 29 (1884) 270; 

Nv. Archt. T. 25 (1884) 309- ; K. S. P. 36 

(1884) i-. 
Meyer, Arnold. Ziir. Vjschr. 42 (1897) 65-; 

D. Mth. Vr. Jbr. 5 (1901) (Heft 1) 18-. 
Meyer, Friedrich. D. Mth. Vr. Jbr. 8 (1900) 

(Heft 1) 59-. 

Miller, Thomas. Edinb. E. S. P. 19 (1893) liv-. 
Minding, Ernst Ferdinand Adolf. Z. Mth. Ps. 

45 (1900) (H.-lt. Ab.) 113-. 
Minich, Serafino Eafaele. Yen. I. At. 1 (1882- 

83) 1095-. 

Minnigerode, B. Lpldina. 32 (1896) 143-. 
Mister, Jean Nicolas. Mathesis 18 (1898) 241. 
Mitchell, Oscar Howard. J. H. Un. Cir. 8 

(1888-89) 110. 
Mobius, August Ferdinand. Arch. Mth. Ps. 49 

(1869) (Lt. B.) clxxxxv. 
Mollinger, Otto. Lpldina. 23 (1887) 54. 
Moigno, (I'abbe) Francois Napoleon Marie. A. 

Tel. 11 (1884) 289; Les Mondes 8 (1884) 

443-; Nt. 30 (1884) 291-. 
Moseley, (Canon) Henry. Nv. Archt. T. 13 

(1872) 328-. 
Mossotti, Ottaviano Fabrizio. As. S. M. Not. 

24 (1864) 87-. 

Moth, Franz Xaver. Wien Aim. (1879) 172-. 
Nagel, Christian Heinrich. Mathesis 7 (1887) 

Nash, Alfred Moses. L. Mth. S. P. 26 (1895) 

557-. ' 
Neumann, Franz Ernst. C. B. 120 (1895) 

1189- ; D. Nf. Vh. (1895) (Th. 1) 27-, (Th. 2, 

Halfte 1) 5-; Elektech. Z. 16 (1895) 353; 

Gott. Nr. (1895) 248-; Nt. 52 1895 176; 

Lpldina. 32 (1896) 51-, 63-; Wien Aim. 46 

(1896) 271- ; D. Mth. Vr. Jbr. 4 (1897) 54-; 
R. S. P. 60 (1897) viii-. 

Newton, Hubert Anson. As. Nr. 141 (1896) 
407- ; Asps. J. 4 (1896) 237; Nt. 54 (1896 
394; Am. J. Sc. 3 (1897) 359-; As. S. M. 
Not. 57 (1897) 228-; N. Y. Am. Mth. S. Bll. 
3 (1897) 169- ; Pop. As. 4 (1897) 236-; E. S. 
P. 63 (1898) i-. 



Biography 0010 

Nobert, Friedrich Adolph. N.-Vorp. Mt. 15 

(1884) 38-. 

Novarese, Enrico. Ev. Mt. 2 (1892) 35. 
Ofterdinger, Felix Ludwia. Bb. Mth. (1896) 

50-; Lpldina. 32 (1896) 103. 
Oliver, James Edward. Nt. 51 (1894-95) 587; 

Science 1 (1895) 544-; Am. Ac. P. 31 (1896) 

367-. 
Olivier, Theodore. A. Cons. Arts et Met. 8 

(1896) 21-. 
Omerique, Antonio Hugo de. Fschr. Mth. 

(1895) 15. 

Oppermann, Ludvig Henrik Ferdinand. Ts. 
Mth. 1 (1883) 137-. 

Orlov, Aleksandr Petrovic. Kazan S. Nt. (Ps.- 
Mth.) P. 7 (1889) 396-. 

Paciuolo, Lucas. Z. Mth. Ps. 34 (1889) (H.-lt. 
Ab.) 81-, 121-. 

Padova, Ernesto. Em. E. Ac. Line. Ed. 5 

(1896) (Sem. 1) 284-. 

Padula, Fortunato. Em. E. Ac. Line. T. 6 

(1882) 30-. 
Palmieri, Luigi. Lpldina. 32 (1896) 147; Nap. 

Ac. Pont. At. 26 (1896) (Necrol. No. 5) 15 pp. ; 

Nap. I. Inc. At. 9 (1896) 12-; Nap. Ed. 35 

(1896) 236-. 

Pankiewicz, Jan. Wiad. Mt. 3 (1899) 302. 
Paolis, Eiccardo de. Palermo Cir. Mt. Ed. 6 

(1892) 208-. 
Parkinson, (Eev.) Stephen. E. S. P. 45 (1889) 

i-; As. S. M. Not. 50 (1890) 167-. 
Peck, William Grey. Eailroad & Eng. J. 66 

(1892) 146. 

Peirce, Benjamin. Pop. As. 3 (1896) 49-. 
Penot, Jean Fleury Achille. Mulhouse S. In. 

Bll. 56 (1886) 505-. 
Perigal, Henry. Aer. J. 2 (1898) 67; L. Mth. 

S. P. 29 (1898) 732-; Nt. 58 (1898) 131; 

Obs. 21 (1898) 282-; Science 7 (1898) 858; 

As. S. M. Not. 59 (1899) 226-; Met. S. QJ. 

25 (1899) 223-. 
Pestalozzi, Ham Jakob. Zur. Vjschr. 41 (1896) 

(Festschr. Th. 1) 123-. 
Pettko, Jdnos. Mag. Tud. Ak. Ets. 3 (1892) 

429-. 
Petzval, Josef. Mh. Mth. Ps. 2 (1891) 480; 

Wien Aim. 42 (1892) 182-. 
Piani, Domenico. Bologna Ac. Sc. Mm. 1 

(1871) 3-. 
Plana, Giovanni Antonio Amedeo. As. S. M. 

Not. 24 (1864) 89-; Edinb. E. S. P. 5 (1866) 

293; Bll. Sc. Mth. As. 5 (1873) 65-; Par. 

Ac. Sc. Mm. 38 (1873) cvii-; Em. S. It. Mm. 

6 (1887) Ixxxvi-. 

Plarr, Gustav. Nt. 45 (1892) 419. 
Plch, Kornel. Casopis 19 (1890) 51-. 
Pliicker, Julius. E. S. P. 17 (1869) Ixxxi-; 

Bll. Sc. Mth. As. 3 (1872) 59-; 5 (1873) 

313- ; Gott. Ab. 16 (1872) 40 pp.; G. Mt. 11 

(1873) 153-. 
Poinsot, Louis. Par. Ac. Sc. Mm. 45 (1899) 

Ixxiii-. 
Poncelet, Jean Victor. A. Cons. Arts et Met. 7 

(1895) 1-. 
Ponte Horta, Francisco da. G. Teix. J. Sc. 14 

(1900) 3-. 
Popov, Aleksandr Thedorovich. Kazan S. Nt. 

(Ps.-Mth.) P. 1 (1883) (No. 9) 13-. 



22 



0010 Biography 

Prediger, Carl. D. Mth. Vr. Jbr. 4 (1897) 51-. 
Price, (Rev.) Bartholomew. Nt. 59 (1898-99) 

229-; As. S. M. Not. 59 (1899) 228-; L. 

Mth. S. P. 30 (1899) 332-; L. Ps. S. P. 16 

(1899) (Ann. Meet.) 10-; Science 9 (1899) 
188; E. S. Yearbook (1900) 185-. 

Prowe, Leopold Friedrich. Z. Mth. Ps. 33 

(1888) (H.-lt. Ab.) 89-. 

Puchewicz, Wtadysiaiv. Wiad. Mt. 3 (1899) 

302. 
Puiseux, Victor Alexandre. Bll. Sc. Mth. As. 

8 (1884) 234-; Par. Ac. Sc. Mm. 44 (1888) 

Ixvii-. 

Quet, Antoine. Les Mondes 9 (1884) 582-. 
Quetelet, Lambert Adolphe Jacques. Amst. 

Ak. Wet. P. (1873-74) (No. 9) 1-; Arch. Sc. 

Ps. Nt. 49 (1874) 350- ; Bll. Sc. Nord 6 

(1874) 62-; Brux. Ac. Bll. 37 (1874) 245-; 

38 (1874) 816- ; Bv. Sc.-Ind. 6 (1874) 38-; 

As. S. M. Not. 35 (1875) 176- ; Edinb. E. S. 

P. 8 (1875) 474-; Mag. Tud. Ak. Ets. 8 

(No. 16) (1875) 241- ; E. S. P. 23 (1875) xi-. 
Quick, (Eev.) Eobert Herbert. Educ. Times 

44 (1891) 185-. 
Eaynard, Arthur Cowper. L. Mth. S. P. 26 

(1895) 554-. 

Eealis, Savin. N. A. Mth. 5 (1886) 200-. 
Eenjifo, Ismael. Santiago de Chile Un. A. 100 

(1898) 527-. 
Eesal, Henri Ame. A. Mines 10 (1896) 625-; 

C. E. 123 (1896) 435-; Liouv. J. Mth. 2 

(1896) 455-; Lpldina. 32 (1896) 147- ; Manch. 
Lt. Ph. S. Mm. & P. 41 (1897) liii. 

Eeuschle, Carl Gustav. Leip. As. Gs. Vjschr. 

10 (1875) 178- ; Z. Mth. Ps. 21 (1876) (H.-lt. 

Ab} 1-. 
Ehodes, Edivard Hawksley. L. Mth. S. P. 26 

(1895) 558. 

Eibaucour, Albert. Mathesis 13 (1893) 270-. 
Eibeiro de Sousa Pinto, Rodrigo. G. Teix. J. 

Sc. 12 (1895) 2-. 
Eiccardi, Pietro. Mod. Ac. Sc. Mm. 2 (1900) 

xxii-. 
Eiemann, Georg Friedrich Bernhard. Gott. 

Nr. (1867) 305- ; Eec. Mth. (Moscou) 3 (1868) 

(Pt. 2) 153- ; K. S. P. 16 (1868) Ixix-. 
Bitter, Ernst. Lpldina. 31 (1895) 218; Nt. 52 

(1895) 600 ; D. Mth. Vr. Jbr. 4 (1897) 52-. 
Eoberts, Samuel Oliver. L. Mth. S. P. 31 

(1900) 282-; Mth. Gz. 1 (1900) 278. 
Eoche, Edouard Albert. C. E. 96 (1883) 1171- ; 

Lille S. Mm. 14 (1885) 17-. 
Eogers, William Augustus. Am. J. Sc. 5 (1898) 

322; As. Nr. 146 (1898) 343-; Asps. J. 7 

(1898) 390- ; Ps. Ev. 6 (1898) 315- ; Science 

7 (1898) 447-. 
Eosenberger, Johann Carl Ferdinand. Elektech. 

Z. 20 (1899) 690; Lpldina. 35 (1899) 182; 

Bb. Mth. 1 (1900) 217-. 
Eossi Ee, Vincenzo de. Em. N. Line. At. 42 

(1889) 83-. 

Eubini, Raffaele. Nap. Ed. 29 (1890) 134- ; 

Nap. Ac. Pont. At. 21 (1891) 275-. 
Sagastume, Demetrio. Arg. S. Ci. A. 47 (1899) 

97-. 
Saint-Venant, Adhemar Jean Claude Barre de. 

A. Pon. Chauss. 12 (1886) 557-; Brux. S. Sc. 



Biography 0010 

A. 10 (1886) (Pt. 1) 77-; C. E. 102 (1886) 

141- ; Nt. 33 (1886) 319-. 
Sandeman, Archibald. Manch. Lt. Ph. S. 

Mm. & P. 8 (1894) 215-. 

Sang, Edward. Edinb. E. S. P. 21 (1897) xvii-. 
Sannia, Achille. Nap. I. Inc. At. 5 (1892) 8-; 

Palermo Cir. Mt. Ed. 6 (1892) 48-; Nap. Ac. 

Pont. At. 24 (1894) (Necrol. No. 2) 6 pp. 
Sarrus, Pierre Frederic. Strasb. Mm. S. Sc. 6 

(1866-70) livr. 1, 12 pp. 
Schaffer, Karl Julius Traugott Hermann. Z. 

Nw. 72 (1899) 393-; Lpldina. 36 (1900) 78-. 
Schapira, Hermann. Lpldina. 34 (1898) 112 ; 

D. Mth. Vr. Jbr. 8 (1900) (Heft 1) 61-. 
Scheeffer, Ludwig. Lpldina. 22 (1886) 56; Z. 

Mth. Ps. 31 (1886) (H.-lt. Ab.) 50-. 
Schellbach, Carl Heinrich. Z. Instk. 12 (1892) 

253 ; Lpldina. 29 (1893) 49-, 75-, 90-, 104-, 

125 . 
Sobering, Ernst Christian Julius. Lpldina. 33 

(1897) 161- ; Nt. 57 (1897-98) 85, 416; As. 

Nr. 145 (1898) 31-; Crelle J. Mth. 119 (1898) 

86; D. Mth. Vr. Jbr. 6 (1899) (Heft 1) 25-. 
Scherk, Heinrich Ferdinand. Lpldina. 21 

(1885) 212-. 
Schjellerup, Hans Carl Frederik Christian. 

Lpldina. 23 (1887) 217; Obs. 10 (1887) 438-; 

Ts. Mth. 5 (1887) 148- ; As. Nr. 118 (1888) 

95-; As. S. M. Not. 48 (1888) 171- ; Nt. 37 

(1888) 154-. 
Schlafli, Ludwig. Bern Mt. (1895) 120- ; Crelle 

J. Mth. 115 (1895) 350; Lpldina. 31 (1895) 

103- ; Em. E. Ac. Line. Ed. 4 (1895) (Sem. 1) 

310-. 
Schober, Karl. D. Mth. Vr. Jbr. 8 (1900) 

(Heft 1) 66-. 
Schols, Charles Mathieu. 's Gravenh. I. Ing. Ts. 

(1896-97) (Verg.) 85-; Amst. Ak. Vs. 5 (1897) 

410. 
Schrentzel, Wilhelm. Z. Mth. Ps. 42 (1897) 

(H.-lt. Ab.) 1-. 
Schroeter, Heinrich Eduard. Crelle J. Mth. 

109 (1892) 358-; Lpldina. 28 (1892) 54; D. 

Mth. Vr. Jbr. 2 (1893) 32-. 
Schulten, Nathanael Gerhard af. Helsingf. 

Acta 6 (1861) 19 pp. 
Seidel, Philipp Ludwig (Ritter) von. As. Nr, 

141 (1896) 319- ; Lpldina. 32 (1896) 138; 

D. Mth. Vr. Jbr. 7 (1899) (Heft 1) 23-. 
Serret, Joseph Alfred. As. Fr. C. E. (1885) 

(Pt. 1) 27; Bll. Sc. Mth. 9 (1885) 123- ; 

C. E. 100 (1885) 673-; N. Antol. Sc. 80 

(1885) 388. 

Serret, Paul. C. E. 127 (1898) 37-. 
Servois, Francois Joseph. Doubs S. Mm. 9 

(1895) 305-. 
Seydler, August. As. Nr. 128 (1891) 15-; 

Lpldina. 27 (1891) 156; Casopis 21 (1892) 

Silva, J. A. Martins da. G. Teix. J. Sc. 6 

(1885) 194-. 
&imerka, Vaclav. Casopis 17 (1888) 253-; 

Fschr. Mth. (1888) 19-. 
Sinram, Heinrich Theodor. D. Mth. Vr. Jbr. 

5 (1901) (Heft 1) 17-. 
Sludskij, Fedor Alekseevic. Eec. Mth. (Mos- 

cou) 20 (1899) 337-. 



23 



0010 Biography 

Smith, Archibald. B. S. P. 22 (1874) i-; 

Edinb. B. S. P. 8 (1875) 282-. 
Smith, Henry John Stephen. Educ. Times 36 

(1883) 96; L. Ps. S. P. 5 (1884) (Ann. Meet. 
1883) 8-; Obs. 6 (1883) 91-; As. S. M. Not. 
44 (1884) 138- ; Met. S. QJ. 10 (1884) 103-. 

Snel van Boyen, Willebrord. Mathesis 4 (1884) 

64. 

Snell, Karl. Lpldina. 22 (1886) 171. 
Sondhauss, Karl Friedrich Julius. Bresl. SI. 

Gs. Jbr. (1886) 324; Lpldina. 22 (1886) 215. 
Spottiswoode, William. Nt. 27 (1883) 597-; 

Obs. 6 (1883) 231- ; Science 2 (1883) 27-; 

As. S. M. Not. 44 (1884) 150- ; C. S. J. 45 

(1884) 628-; L. Ps. S. P. 5 (1884) (Ann. 
Meet. 1884) 8-; Peterm. Mt. 30 (1884) 105; 
B. S. P. 38 (1885) xxxiv-; L. Mth. S. P. 31 
(1900) 283-. 

Stahl, Wilhelm. Lpldina. 30 (1894) 110 ; Crelle 

J. Mth. 114 (1895) 45-; D. Mth. Vr. Jbr. 4 

(1897) 36-. 
Stanecki, Tomasz. Kosmos (Lw.) 16 (1891) 

25-. 

Staudigl, Rudolf. Mh. Mth. Ps. 2 (1891) 480. 
Staudt, Karl Georg Christian von. Kharkov 

Mth. S. Com. (1880) 167-. 
Steen, Adolph. Lpldina. 22 (1886) 219; Ts. 

Mth. 4 (1886) 65-. 
Steichen, Michel. Brux. Ac. Bll. 21 (1891) 

308-. 
Steiner, Jacob. Sch. Nf. Gs. Vh. 56 (1873) 

215- ; A. Mt. 7 (1875-76) 65-; Bb. Mth. 1 

(1900) 129-. 
Stern, Moriz Abraham. Zur. Vjschr. 39 (1894) 

131- ; Munch. Ak. Sb. 24 (1895) 142; D. 

Mth. Vr. Jbr. 4 (1897) 34-. 
Stieltjes, Thomas Joliannes (jun.). Lpldina. 

31 (1895) 56; Toul. Fac. Sc. A. 9 (1895) 

Storch'i, Felice. Mod. Ac. Sc. Mm. 8 



Strehlke, Friedrich Samuel. Danzig Schr. 6 

(Heft 4) (1887) 173-. 
Streintz, Heinrich. Lpldina. 28 (1892) 210; 

Steierm. Mt. (1892) 233-. 
Strong, Theodore. Am. Ac. P. 8 (1873) 228-. 
Svanberg, Adolf Ferdinand. Stockh. Vt. Ak. 

Lefn. 1 (1869-73) 111-. 
Sylvester, James Joseph. J. H. Un. Cir. 8 

(1888-89) 23-; [16 (1896-97)] 25-, 53-; [18 

(1898-99)] 29; Nt. 55 (1896-97) 492-; Am. 

J. Mth. 19 (1897) (Suppl.) 1 p. ; Lpldina. 33 

(1897) 90- ; Manch. Lt. Ph. S. Mm. & P. 41 

(1897) liii-; Mathesis 17 (1897) 245-; Nap. 

Bd. 36 (1897) 165- ; N. Y. Am. Mth. S. Bll. 

3 (1897) 299-; Science 5 (1897) 597-; Wiad. 

Mt. 1 (1897) 175- ; I. Act. J. 33 (1898) 345-; 

Kazan S. Ps.-Mth. Bll. 7 (1898) (Prot.) 89-; 

Mth. A. 50 (1898) 133- ; B. S. P. 63 (1898) 

Tartaglia, Nicolb, biographical sketch. Tonni- 
Bazza, V. Brescia At. Cm. (1900) 160-. 

Taylor, William Bower. Wash. Ph S. Bll 13 
(1900) 418-. 

Terrot, (Bishop) Charles Hughes. Edinb. B. 
S. P. 8 (1878) 9-. 

Tesla, Nikola. Casopis 19 (1890) 155-. 



Biography 0010 

Tillol, Jules Jerdme. Toul. Ac. Sc. Mm. 3 

(1891) 525-. 
Timmermans, Jean Alexis. Arch. Mth. Ps. 49 

(1869) Lt. B. 294. 
Todhunter, Isaac. Nt. 29 (1884) 436 ; B. S. P. 

37 (1884) xxvii-; As. S. M. Not. 45 (1885) 

194- . 
Tortolini, Barnaba. Arch. Mth. Ps. 44 (1865) 

clxxv-; 45 (1866) clxxvii; Bll. Sc. Mth. As. 

8 (1875) 272-; Bm. N. Line. At. 28 (1875) 

93-; A. Mt. 7 (1876) 63-; Bm. S. It. Mm. 6 

(1887) Ixv-. 
Transon, Abel Etienne Louis. A. Mines 14 

(1878) 433-. 

Trudi, Nicola. G. Mt. 22 (1884) 304- ; Nap. 

I. Inc. At. 3 (1884) 5-; Nap. Ed. 23 (1884 

149-; Nap. Ac. Pont. At. 16 (Ft. 1) (1885) 

243-. 
Turazza, Domenico. Yen. I. At. 1 (1898-99) 

(Pt. 1) 69-. 
Ullhers, Jolmnn Konrad. Lpldina. 23 (1887) 

215. 
Unverzagt, Wilhelm. Z. Mth. Ps. 31 (1886) 

(H.-lt. Ab.) 41-. 
Villas, Antal. Mag. Tud. Ak. Ets. 8 (No. 17) 

(1875) 260-. 
Vega, Georg von. Z. Mth. Ps. 39 (1894) (H.-lt. 

Ab.) 204-. 
Venturoli, Giuseppe. N. A. Sc. Nt. 8 (1847) 

5-, 185-. 
Verdam, Gideon Jan. Amst. Jb. Ak. (1866) 

56-; Arch. Mth. Ps. 46 (1866) Lt. B. clxxxiii. 
Vervaet, Julian. Casopis 15 (1886) 25-. 
Victorica y Soneyra, Jos6. Arg. S. Ci. A. 36 

(1893) 265-. 

Vicuna, Gumersindo. Bb. Mth. (1891) 33-. 
Vincent, Alexandre Joseph Hidulphe. Lille S. 

Mm. 6 (1869) 561-. 
Volpicelli, Paolo. Bm. B. Ac. Line. T. 3 

(1879) 160-. 

Vydra, Stanislav. Casopis 1 (1872) 1-, 49-. 
Walker, John James. Nt. 61 (1899-1900) 618. 
Wappler, Hermann Emil. Bb. Mth. 1 (1900) 

225. 
Weierstrass, Karl Theodor Wilhelm. Nt. 55 

(1896-97) 443; Acta Mth. 21 (1897) 79-; 

Bologna Ed. 1 (1897) 101- ; C. E. 124 (1897) 

430- ; Crelle J. Mth. 117 (1897) 357 ; Lpldina. 

33 (1897) 54-; Nap. Bd. 36 (1897) 63-; St. 

Pet. Ac. Sc. Bll. 6 (1897) xxxv-; Wiad. Mt. 

1 (1897) 53-; Wien Aim. 47 (1897) 304- ; 

Munch. Ak. Sb. 27 (1898) 402- ; D. Mth. Vr. 

Jbr. 6 (1899) (Heft 1) 27-. 
Weninger, Vincze. Mag. Tud. Ak. Etk. (Mth.) 

1 (1881) (No. 10) 22 pp. 
Weyer, Georg Daniel Ediiard. Nt. 55 (1896-97) 

299; As. Nr. 142 (1897) 343-; Lpldina. 33 

(1897) 49 ; D. Mth. Vr. Jbr. 6 (1899) (Heft 1) 

Weyr, Emil. Lpldina. 30 (1894) 57; Wien 
Aim. 44 (1894) 244-; Casopis 24 (1895) 163- ; 
Fschr. Mth. (1895) 32-; Mh. Mth. Ps. 6 
(1895) 1-; Palermo Cir. Mt. Ed. 9 (1895) 
260- ; D. Mth. Vr. Jbr. 4 (1897) 24-. 

Whewell, (Dr) William. Ausl. 39 (1866) 304- ; 
Gg. S. J. 36 (1866) cxxii-; As. S. M. Not. 
27 (1867) 110- ; B. S. P. 16 (1868) li-. 



24 



0020 Periodicals 

Wiener, Ludwig Christian. Lpldina. 32 (1896) 

136-, 155-, 166- ; D. Mth. Vr. Jbr. 6 (1899) 

(Heft 1) 46-. 

Williams, J. Hill. I. Act. J. 26 (1887) 218-. 
Wiltheiss, Ernst Eduard. Lpldina. 36 (1900) 

135. 
Winckler, Anton. Lpldina. 28 (1892) 162 ; Mh. 

Mth. Ps. 3 (1892) 403- ; Wien Aim. 43 (1893) 

257-. 
Wolf, Joh. Rudolf. Bern Mt. (1893) 193- ; 

Lpldina. 29 (1893) 211 ; Nt. 49 (1893-94) 163, 

266-; As. J. 13 (1894) 181- ; As. Nr. 134 

(1894) 183- ; As. S. M. Not. 54 (1894) 206- ; 
Ziir. Vjschr. 39 (1894) 1-. 

Wolstenholme, Joseph. Nt. 45 (1892) 85. 
Wood, De Volson. Science 6 (1897) 204-. 
Woolhouse, Wesley Stoker Barker. As. S. M. 

Not. 54 (1894) 204- ; I. Act. J. 31 (1895) 

362-. 
Woolley, Joseph. Nt. 39 (1889) 517; Nv. 

Archt. T. 30 (1889) 463-. 
Worpitzky, Julius. D. Mth. Vr. Jbr. 4 (1897) 

Wren,' Walter. L. Mth. S. P. 29 (1898) 731-. 
Yvon-Villarceau, Antoine Joseph Francois. Ciel 

et Terre 5 (1885) 20-, 72 ; Par. Ac. Sc. Mm. 

45 (1899) i-. 

Zajaczkowski, Wtadystaw. Wiad. Mt. 2 (1898) 
V 258-. 
Zbikovskij, Anton Ksaverjevict. Wiad. Mt. 4 

(1900) 268 ; Kazan S. Ps.-Mth. Bll. 10 (1901) 

(Prof.) 39-; Fschr. Mth. (1900) 31. 
Zeipel, Ewald Victor Ehrenhold von. Lpldina. 

29 (1893) 111. 
Zetzsche, Karl Eduard. Dresden Isis Sb. (1894) 

17-; Elektech. Z. 15 (1894) 297-; Giving. 41 

(1895) 185-. 

Zillmer, August. D. Mth. Vr. Jbr. 4 (1897) 
, 23-. 

Zmurko, Waicrzyniec (Laurent). Kosmos (Lw.) 
14 (1889) 169- ; Lpldina. 26 (1890) 52 ; Prace 
Mt.-Fiz. 2 (1890) 423-. 

0020 Periodicals. Reports of In- 
stitutions, Societies, Congresses, etc. 

Belgian Eoyal Academy, secular report. 1772- 
1872. Tilly, J. M. de. Brux. Ac. Cent. 
Anniv. 2 (1872) 200 pp. 

British Association. Elliptic and hyper-elliptic 
functions, reports on progress. Russell, 
W. H. L. B. A. Ep. 39 (1869) 334-; 40 
(1870) 102- ; 42 (1872) 334-; 43 (1873) 307-. 

. Fundamental invariants of algebraic 

forms, reports of committee for calculating 
tables. B. A. Ep. (1880) 38-; (1881) 55-; 
(1882) 37-. 

. Geometrical elementary instruction, 
report of Committee. B. A. Ep. (1876) 8-. 

. Mathematical notation and printing, 

report of Committee. B. A. Ep. (1875) 337-. 

. Sciences in Belgium, report. 
Quetelet, L. A. J. B. A. Ep. (1835) 35-; 
Quetelet Cor. Mth. 9 (1837) 1-. 

. tables, reports. B. A. Ep. (1873) 

1-; (1875) 305- ; (1878) 172- ; (1879) 46-; 
(1880) 30- ; (1881) 303- ; (1883) 118-. 



General Treatises 0030 

British Association. Mathematics and physics, 

progress, report of Committee. B. A. Ep. 

(1879) 37-. 
Marburg University Math. - phys. Institute. 

Gerling, C. L. Grunert Arch. 2 (1842) 212-. 
Paris Academy of Sciences, reports on papers, 

&c. 1816-19, 1821. Delamlre, J. B. J. 

Par. Mm. Ac. Sc. 1 (1816) (H.) 1-; 2 (1817) 

(H.) 1-; 3 (1818) (H.) 1-; 4 (1819-20) (H.) 

1-, 127- ; 5(1821-22) (H.) 1-. 
, , . 1822-28. Fourier, 

J. B. J. Par. Mm. Ac. Sc. 5 (1826) (H.) 



231- ; 6 (1827) (H.) 1-; 7 (1827) (H.) 1-; 
8 (1829) (H.) 1-; 9 (1830) (H.) 1-; 10 (1831) 
(H.)l-; 11 (1832) (H.) 1-. 

, L'Institut, reports in mathematics and 
physics. Delambre, J. B. J. J. de Ps. 53 
(1801) 380- ; 61 (1804) 81-; 82 (1816) 189-. 

, , , 1805-1815. Delambre, 

J. B. J. Par. Mm. de PI. (1806) Sem. 2 
(H.) 1-; (1807) Sem. 2 (H.) 1-; (1808) (H.) 
1-; (1809) (H.) 1-; (1810) (pte. 2) (H.) i- ; 
(1811) (H.) i- ; (1812) (H.) i- ; (1815) (H.) 1-. 

Philosophical Congress, Mathematics at the. 
Couturat, L. Ens. Mth. 2 (1900) 397-. 

Statistical Congress, Fifth and sixth Inter- 
national, reports. Brown, S. Assur. Mg. 
11 (*1864) 195- ; I. Act. J. 14 (*1869) 165-. 

0030 General Treatises, Text 
Books, Dictionaries, Tables, 
Collected Works. 

Analysis, report. Peacock, G. B. A. Ep. 

(1833) 185-. 
Bombelli, Eafael, supposed 2nd edition of his 

algebra. Favaro, A. Bb. Mth. (1893) 15-. 
, , . Riccardi, P, Bb. 

Mth. (1893) 64. 
Books of arithmetic and algebra of 16th century. 

Fontes, . Toul. Ac. Sc. Bll. 



' ' Geometrical Eesearches, ' ' Introduction. Gar- 
diner, M. N. S. W. Ph. S. T. 1 (1866) 61-. 
Hebrew codex, Mathematical and astronomical 

writings. Riccardi, P. Bb. Mth. (1893) 

54-. 
translations of mathematical works. Stein- 

schneider, M. Bb. Mth. (1893) 51-. 
Hug's "Mathematik," remarks. Schlafli, L. 

Ziir. Vjschr. 7 (1862) 366-; 8 (1863) 79. 
Huygens, " Exercitationes Mathematics. " 

Biot, J. B. J. Sav. (1834) 291-. 
Infinitesimal calculus, account of text books 

from Euler to present time. Bohlmann, G. 

D. Mth. Vr. Jbr. 6 (1899) (Heft 2) 91-. 
Journalism, mathematical, in England. 

Mackay, J. S. As. Fr. C. E. (1893) (Ft. 2) 

303-. 
Lagrange's " Me"canique Analytique," Poinsot's 

corrections criticised. Breton (de Champ), P. 

Liouv. J. Mth. 1 (1875) 81-, 263-. 
, justified. Bertrand, J. Liouv. 

J. Mth. 1 (1875) 181-. 
Lhuilier's " Elements d'analyse, &c." Ger- 

gonne, J. D. Gard Not. Tr. Ac. (1810) 196-. 



25 



0032 Bibliographies 

Mathematical text books. Feyerabendt, . 

D. Nf. Tbl. (*1880) 138. 
Military text book of trigonometry, note on a. 

Ostrogradsky, . [1851] St P6t. Ac. Sc. Bll. 

10 (1852) 11-. 
Eaabe's, " Math. Mittheilungen," remarks and 

additions. Schlqfti, L. [1857] Ziir. Vjschr. 

3 (1858) 23-. 
Bamsing's and Holten's works, remarks. 

Lorenz, L. Mth. Ts. 3 (1861) 161-. 



Tabulation of I sin 



fir); 



Lindman, C. F. 



Ups. S. Sc. N. Acta 14 (1891) No. 1, 15 pp. 
Treatise on Use of Higher Mathematics. Euler, 

L. [1741] Crelle J. 35 (1847) 106-. 
Trisection of the angle, rare book on. Valentin, 

G. Bb. Mth. (1893) 113-. 
Vega's " Thesaurus Logarithmorum," notes on. 

Gauss, C. F. As. Nr. 32 (1851) 181-. 
Wronski's theory of numbers. Dickstein, S. 

Krk. Ak. (Mt.-Prz.) Ez. 4 (1893) 73-, ? 396; 

Crc. Ac. Sc. Bll. 1892, 64-. 

0032 Bibliographies. 

Aggregates, progress of theory 1893-99. 

Vivanti, G. Bb. Mth. 1 (1900) 160-. 
Algebraic equations, history of proof of root 

existence. Loria, G. Ev. Mt. 1 (1891) 185- ; 

2(1892)37-; 3(1893) 105-. 
__ . , investigations concerning existence of 

roots. Loria, G. Bb. Mth. (1891) 99-. 
Bernoulli's numbers. Ely, G. S. Am. J. Mth. 

5 (1882) 228-. 
" Biblioteca Matematica Italiana." Favaro,A. 

[1880] Yen. I. At. 7 (1881) 47-. 
. Eiccardi, P. Bologna Ac. Sc. Mm. 

10 (1889) 635-. 
Decimal calculation. Terquem, O. N. A. Mth. 

12 (1853) 195-. 
Determinants. Muir, T. QJ. Mth. 18 (1882) 

110- ; 21(1886)299-. 
Differential equations. Mansion, . Brux. S. 

Sc. A. 15 (1891) (Pt. 1) 32-, 60, 105. 
Distributive operations. Pincherle, S. Bb. 

Mth. (1899) 13-. 
Euclid. Eiccardi, P. Bologna Ac. Sc. Mm. 

8 (1887) 401- ; 9 (1888) 321- or 111-; 1 

(1890)27-; 3(1892)639-. 
, two editions of 1482. Valentin, G. Bb. 

Mth. (1893) 33-. 
Euler's works, new list. Hagen,J.G. D. Mth. 

Vr. Jbr. 5 (1901) (Heft 1) 82-. 
writings. Valentin, G. Bb. Mth. (1898) 

Geometry in n dimensions, index of memoirs. 

Schlegel, V. Lpldina. 22 (1886) 160- ; Ens. 

Mth. 2 (1900) 77-. 
, triangle. Vigarie, E. As. Fr. C. E. (1895) 

(Pt. 2) 50-. 
"Histoire de la perspective," certain Italian 

works omitted. Eiccardi, P. Bb. Mth. 



History of mathematics, Danish. Christensen, 
S. A., & Heiberg, J. L. Bb. Mth. (1889) 



75-. 



Tables of Functions 0035 

History of mathematics, Dutch. Bierens de 
Haan, D. Bb. Mth. (1891) 13-. 

Italian. Favaro, A. Bb. Mth. (1892) 

67-. 

, Norwegian. Hoist, E. Bb. Mth. 

(1889) 97-. 

, Polish. Dickstein, S. Bb. Mth. 

(1889) 43-; Prace Mt.-Fiz. 2 (1890) 247-; 3 
(1892) 184-. 

, Portuguese. Teixeira, F. G. Bb. 

Mth. (1890) 91-. 
, Spanish. Vicuna, G. Bb. Mth. 

(1890) 13-. 

, Swedish, 1667-1888. Enestrom, G. 

Bb. Mth. (1889) 1-. 
, Swiss. Suter, H. Bb. Mth. (1890) 

97-. 
Hyperspace and non-Euclidean geometry. 

Halsted, G. B. Am. J. Mth. 1 (1878) 261-, 

384-; 2(1879) 65-. 
Imseneckij, Vasilij Grigorjevi5, list of works. 

Kharkov Mth. S. Com. 3 (1893) 290-. 
Line geometry and its applications. Koenigs, G. 

Toul. Fac. Sc. A. 3 (1889) 24 pp. ; 6 (1892) 

67 pp. ; 7 (1893) 55 pp. 
Linear differential equations. Nixon, H. B., 

d- Fields, J. C. Am. J. Mth. 7 (1885) 353-. 
Mathematical bibliographies. Enestrom, G. 

Bb. Mth. (1890) 37-. 

bibliography, latest work in. Enestrom, G. 
Bb. Mth. (1897) 65-. 

MSS. in Amplonian collection. Stein- 
schneider, M. Bb. Mth. (1890) 65- ; (1891) 
41-, 65-. 

publications (review). Favaro, A. Ven. I. 
At. (1892-93) 829-. 

work, extracts from, with complete list of 
author's publications. Catalan, E.G. Liege 
S. Sc. Mm. 12 (1885) No. 2, 407 pp.; 13 
(1886) 404 pp. ; 15 (1888) No. 1, 275 pp. 

Numbers, theory. Stieltjes, T. J. Toul. Fac. 

Sc. A. 4 (1890) 103 pp. 
Nuncius Sidereus, Prague edition. Wohlwill, 

E. Bb. Mth. (1887) 100-. 
Eussian physics and mathematics. Bobynin, 

V. V. Fschr. Mth. (1887) 2. 
Sacrobosco's algorithm. Curtze, M. Bb. Mth. 

(1895) 36-. 
, certain editions. Eiccardi, P. Bb. Mth. 

(1894) 73-. 
Surfaces and twisted curves. Hill, J. E. N. Y. 

Am. Mth. S. Bll. 3 (1897) 133-. 
Women and the exact sciences. Valentin, G. 

Bb. Mth. (1895) 65-. 
. Enestrom, G. Bb. Mth. (1896) 

73-. 

0035 Tables of Mathematical 
Functions. 

Abscissae and ordinates of points on an arc of 

a circle 1 m. radius, for intervals of 1 cm. 

Cretin, . (vn) A. Cond. Pon. Chauss. 6 

(1862) 251-. 
Advantages in using tables. Buzengeiger, 

K. H. J. Lindenau Z. 2 (1816) 23-. 



26 



0035 Tables of Functions 

Annuity-value coefficients. Searle, T. J. I. 

Act. J. 28 (1890) 192-. 
Arc radius and chord. Sigaud, . (vm) A. 

Cond. Pon. Chauss. 1 (1857) 132- . 
Arcs, tangents and chords. Sigaud, . (vm) 

A. Cond. Pon. Chauss. 2 (1858) 122-. 
Bernoulli's numbers, first 40 logarithms. 

Thoman, F. C. E. 50 (1860) 905-. 

, 62. Adams, J. C. [1877] Crelle J. 

Mth. 85 (1878) 269-. 

, 250, and their logarithms. Glaisher, 
J. W. L. [1871-72] Camb. Ph. S. T. 12 
(1873) 384-. 

Bessel equation, roots. Willson, E. W., & 
Peirce, B. 0. N. Y. Am. Mth. S. Bll. 3 
(1897) 153-. 

, solution. Aldis, W. S. B. S. P. 64 

(1899) 203-. 

functions J (k) and J t (k) (or 1\ and I' k ) 
from k = to k = 15-5. Meissel, E. Berl. 
Ak. Ab. (1888) (Anh. Mth.) 23 pp. 

, (2nd and 3rd Eeports.) Brit. Ass. Comm. 

B. A. Ep. (1893) 227-; (1896) 98-. 
Binary duodecimic, generating functions and 

groundforms. Sylvester, J. J. Am. J. Mth. 
4 (1881) 41-. 

sextic. Cayley, A. Am. J. Mth. 4 (1881) 
379-. 

Brigg's log. n\ Jarolimek, C. Casopis 15 

(1886) 70-; Fschr. Mth. (1886) 1123. 
Calza's "tables of constants" to facilitate 

multiplication and division. Baravelli, G. C. 

Z. Mth. Ps. 44 (1899) 50-. 
Complex prime factors, formed from 5th roots 

of unity, of primes of form 5/u + l. Eeuschle 

[C. G.]. Berl. Mb. (1859) 488-. 
, 7th roots of unity, of primes up 

to 1000. Eeuschle [C. G.]. Berl. Mb. (1859) 

694-. 
, llth roots of unity, of primes 

up to 1000. Eeuschle [C. G.]. Berl. Mb. 

(1860) 190-. 
, 13th roots of unity, of primes 

up to 1000. Eeuschle [C. G.]. Berl. Mb. 

(1860) 194-. 
, 17th roots of unity, of primes 

up to 1000. Eeuschle [C. G.]. Berl. Mb. 

(1860) 714-. 
, 19th roots of unity, of primes 

up to 1000. Eeuschle [C. G.]. Berl. Mb. 

(1860) 719-. 
, 23rd roots of unity, of primes 

up to 1000. Eeuschle \C. G.]. Berl. Mb. 

(1860) 725-. 
, 29th roots of unity, of primes 

up to 1000. Eeuschle [C. G.]. Berl. Mb. 

(1860) 729-. 
Compound interest. Weninger, V. (xn) Mag. 

Ak. Ets. (Mth. Term.) 6 (1865) 207-. 
Congruence M= a a b? (Mod. N), specimen table. 

Cayley, A. QJ. Mth. 9 (1868) 95-. 
Connecting curves (on railroads). Eibette, . 

(vra) A. Cond. Pon. Chauss. 5 (1861) 

108-. 
Cremona's transformation between two planes. 

Eoberts, S. [1872] L. Mth. S. P. 4 (1871- 

73) 121-. 



Tables of Functions 0035 

Cube roots of primes to 31 places. Drach, 
S. M. [1877] Mess. Mth. 7 (1878) 86-. 

Definite integrals. Bierens de Haan, D. Amst. 
Vh. 5 (1858) 1-. 

, (Bierens de Haan's). Bellavitis, G. 
Yen. At. (1858-59) 423-. 

, supplement. Bierens de Haan, D. 
[1861] Amst. Vh. Ak. 10 (1864) 92 pp. 

A m O"-MI(m). Cayley, A. [1879] Camb. Ph. 

S. T. 13 (1883) 1-. 
Differential equations. Adams, Jas. Thomson 

A. Ph. 10 (1817) 116-. 
Elliptic arcs, Schmidt's. Verdam, G. J. Amst. 

I. (1842) 57-. 

Empirical formulae, tables for facilitating de- 
termination. Hale, A. W. Am. J. Mth. 5 

(1882) 342-. 
Equation msin 4 2 = sin (z - q), table for solving. 

Gasparis, A. de. As. Nr. 78 (1872) 177-. 
Errata in several tables. Stanley, A. D. Silli- 

man J. 5 (1848) 398-. 

Exponential function e x , to 12 places of deci- 
mals. Newman, F. W. [1887] Camb. Ph. 

S. T. 14 (1889) 237-. 
Factor tables and formation of table for fourth 

million. Glaisher, J. W. L. [1878] Camb. 

Ph. S. P. 3 (1880) 99-, 228-. 
, Kulik's (report). Petzval, J. Wien Sb. 

53 (1866) (Ab. 2) 460- . 
Formulae and numerical tables, collection. 

Hoiiel, J. Bordeaux Mm. S. Sc. 4 (cah. 2) 

(1866) i-. 
Fractions, with note on number of divisions 

required to find G.C.M. Hill, C. J. D. Lund 

Acta Un. 2 (1865) (Mth.) No. 1, 16 pp. 
Function, transcendental. Buzengeiger, K. H. J. 

Zach M. Cor. 24 (1811) 583-. 

<r(n) in theory of numbers. Mertens, F. 
Wien Ak. Sb. 106 (1897) (Ab. 2 a) 761-. 

G (r, v)-integrals. Brit. Ass. Comm. (Pearson, 

K.). B. A. Ep. (1899) 65-. 
Gaussian. Gould, B. A. Am. As. P. (1849) 

362-. 
. Grunert, J. A. Grunert Arch. 30 (1858) 

233-. 

Gauss's antilogarithmic tables, statements con- 
cerning. Gray, P. Assur. Mg. 7 (*1858) 

350-. 
Geometry of numbers, with a table of squares 

of numbers up to 10,000. Preobraschensky, 

P. W. Fschr. Mth. (1886) 135. 
Goldbach's law concerning prime numbers. 

Haussner, E. Ac. Nt. C. N. Acta 72 (1899) 1-. 
Graphic, for computation. Gilbert, G. K. 

Smiths. Misc. Col. 25 (1883) Art. 2, 3 pp.; 

(Wash. Ph. S. Bll. 5 (1883).) 
, examples. Mehmke, E. Z. Mth. Ps. 44 

(1899) 56-. 
Hyperbolic functions, some errors in tables. 

Lampa, E. [1892] Tor. Ac. Sc. At. 32 

(1896) 350- or 530-. 

sectors, and logs, of their sines and cosines. 
Gronau, J. F. W. Danzig Schr. 6 (Heft 4) 
(1862). 

Improvement, suggestion for. Macdonald, 
W. J. Edinb. Mth. S. P. 13 (1895) 144-. 

Integrals, appendix. Bierens de Haan, D. 
Amst. Ak. Vh. 22 (1883) (No. 2) 225 pp. 



27 



0035 Tables of Functions 

Interest, Smart's. Wilding, R. I. Act. J. 22 

(*1881) 129-. 
, universal. Goodwyn, H. Nicholson J. 4 

(1801) 433-. 
Least primitive roots of all odd primes under 

3000. Wertheim, G. Acta Mth. 17 (1893) 

315- ; 20 (1897) 157; 22 (1899) 200. 
. primes between 3000 and 5000. 

Wertheim, G. Acta Mth. 20 (1897) 153- ; 22 

(1899) 200. 

primitives of prime numbers. Le Besgue, 
V. A. Bordeaux Mm. S. Sc. 3 (cah. 2) 
(1865) 231-. 

Log. sin. and log. tan. of small arcs. Drach, 
S. M. As. S. M. Not. 21 (1861) 147-. 

Logarithm-integral, exponential integral, and 
other Eulerian integrals. Bellavitis, G. 
[1873] Yen. I. Mm. 18 (1874) 125-. 

MS., 12 figure, from 1 to 120,000, by Thom- 
son, presented to B. A. S. Glaisher, J. W. L. 
As. S. M. Not. 34 (1874) 447-; 35 (1875) 
135. 

Logarithmic. Shortrede, It. Beng. J. As. S. 

I (1842) 40-. 

. Glaisher, J. W. L. As. S. M. Not. 33 

(1873) 440-. 
, abridged, Burnier's simplification of 

Flower's method. Hoiiel, J. Bordeaux Mm. 

S. Sc. 8 (1870) 188-. 
, Callet's, errors in. Lefort, F. C. E. 44 

(1857) 1097-. 
, , . Secretan, . C. E. 44 (1857) 

1276-. 
, , . Dupuis, . C. E. 45 (1857) 

, ', . Schols, C. M. Delft EC. Pol. A. 

3 (1887) 130-. 
, , 2nd, correction. Herrmann, . Wien 

SB. (1848) 113-. 
, errata in. Galbraith, W. As. Nr. 23 

(1846) 109-. 
, . Wackerbarth, A. D. As. S. M. 

Not. 27 (1867) 253-. 
, certain. Mendlzdbal Tamborrel, J. de. 

Mex. S. "Alzate" Mm. 5 (1891) (Rv.) 9-. 
, facilities of certain. Gray, P. Assur. Mg. 

II (* 1864)230-. 

and factor, with especial reference to 
Drach's suggestion. Glaisher, J. W. L. 
(vii) [1873] Mess. Mth. 3 (1874) 7-. 

, formulae for. Merri field, C. W. Assur. 

Mg. 6 (*1857) 298-. 
, index of sketch for. Bierens de Haan, D. 

Amst. Ak. Vh. 15 (1875) 35 pp. 

to more than 7 places, utility. Govi, G. 
Tor. At. Ac. Sc. 8 (1872-73) 157-. 

, note on some. Mendizdbal Tamborrel, J. 

de. Mex. S. "Alzate " Mm. 1 (1887) 223-. 
, of 1849, errata. Shortrede, R. As. S. M. 

Not. 27 (1867) 272-. 

sines, construction of canon. Sang, E. 
Edinb. E. S. P. 12 (1884) 601-. 

, suggestions. Hanlon, G. O. (vn) 118731 
Mess. Mth. 3 (1874) 100-. 

and trigonometric. Folie, F. Liege Mm. S. 

, Vega, errata. Kulik, J. P. As. Nr. 3 
(1825) 191-. 



Tables of Functions 0035 

Logarithmic, Vega, errata. Bremiker, (Prof.) 

. As. Nr. 85 (1875) 373-. 
, Vlacq's (or Briggs'), errors in. Glaisher, 

J. W. L. As. S. M. Not. 32 (1872) 255-, 

288-. 
, ( ), . Sang, E. Edinb. E. S. 

P. 8 (1875) 371- ; Nt. 42 (1890) 593. 
Logarithms and anti-logarithms to ten places, 

formation. McKenzie, D. J. McG. I. Act. 

J. 24 (1884) 243-. 
, , (note on McKenzie's 

paper). Hardy, G. F. I. Act. J. 24 (1884) 

252-. 
twelve places. Gray, P. Assur. 

Mg. 12 (*1866) 71-, 121-, 212-, 252-. 
, to calculate. Perry, J. Nt. 59 (1898-99) 

393, 439. 

, . Dufton, A. Nt. 61 (1899-1900) 415. 

, . Perry, J. Nt. 61 (1899-1900) 415-. 

of circular and hyperbolic functions. Forti, 
A. Pisa A. Un. Tosc. Sc. Cosm. 6 (1861) 
5. 

, error in a seven figure set. Sang, E. I. 
Act. J. 17 (*1873) 142, 300-. 

of sum and difference of two numbers. 
Hill, N. Franklin I. J. 140 (1895) 130-. 

, ten place. Chislwlm, J. I. Act. J. 26 

(1887) 55-. 
of vulgar fractions, with numerator and 

denominator not over 100. Airy, G. B. 

I. CE. P. 65 (1881) 271-. 
Manuscript table of Napierian logarithms, sines 

&c. Pearson, J. B. [1878] Camb. P"h. S. P. 

3 (1880) 146-. 
Mathematical functions, certain. Brit. Ass. 

Comm. B. A. Ep. (1898) 145. 
Method for extending accuracy of tables. 

Sheppard, W. F. [1899] L. Mth. S. P. 31 

(1900) 423-. 

Multiplication by table of single entry. Syl- 
vester, J. J. Assur. Mg. 4 (*1854) 236-. 
. Glaisher, J. W. L. Ph. 

Mg. 6 (1878) 331-. 

table, oldest. Ebert, R. Dresden Isis Sb. 
(1896) (Ab.) 44-. 

Napierian logarithm of IT to 30 decimal places. 
Glaisher, J. W. L. QJ. Mth. 25 (1891) 362-, 
384. 

logarithms of 2, 3, 5, 7 and 10. Adams, 
J. C. E. S. P. 42 (1887) 22-. 

Natural logarithms of Nos. 1-25 to 81 places. 
Vietz, . As. Nr. 4 (1826) 53-. 

trigonometrical ratios, and inverses of num- 
bers. Folie, F. Liege S. Sc. Mm. 9 (1882) 
No. 2, 11 pp. 

Numbers 1-4100 partitioned into 2 squares. 

Bretschneider, C. A. [1851] Crelle J. 46 

(1853) 1-. 
Numerical table, and application to certain 

transcendentals. Catalan, E. Brux. Ac. 

Mm. 47 (1889) No. 3, 26 pp. 

tables to assist in change of coordinates. 
Vinot, . C. E. 101 (1885) 938-. 

, new method of arranging. Dittmar, W. 

Ph. Mg. 21 (1861) 137-. 

value of fe^dx. Daicson, H. G. L. Mth. 
S. P. 29 (1898) 519-. 



28 



0035 Tables of Functions 

Odd numbers 1-191 divided into square numbers. 
Pollock, (Sir) F. [1853] Phil Trans. (1854) 
311-. 

, products of all, from 11 to 99 to 3 
figures. Anon. Brux. Obs. A. (As.) 7 (1896) 
[at end of vol.}. 

Prime factors, decomposition of numbers into. 

Le Besgue, V. A. Bordeaux Mm. S. Sc. 3 

(cah. 1) (1864) 1-. 
, discovery. Hill, C. J. D. Crelle J. 12 

(1834) 355-. 
Primitive roots. Kulik, J. P. Crelle J. 45 

(1853) 55-. 
of primes from 3 to 101. Crelle, A. L. 

Crelle J. 9 (1832) 27-. 
of prime numbers. Ostrogradsky, M. A. 

[1836] St Pet. Ac. Sc. Mm. 3 (1838) 359-. 
Prony's logarithmic and trigonometrical tables. 

Sang, E. [1874] Edinb. R. S. P. 8 (1875) 

421-. 

table of logarithms (Eeply to Lefort). Sang, 
E. Edinb. R. S. P. 8 (1875) 581-. 

Proportional logarithms. Shortrede, E. Beng. 
J. As. S. 10 (1841) 713-. 

parts, Vega's. Hartmann, J. Grunert Arch. 
31 (1858) 63-. 

Pythagorean triangle. Bretschneider, C. A. 

Grunert Arch. 1 (1841) 96-. 
Quadratic binary forms. Cayley, A. [1860] 

Crelle J. 60 (1862) 357-. 

equations with real roots. Mehmke, R. 
Z. Mth. Ps. 43 (1898) 80-. 

ternary forms, reduced positive. Eisen- 
stein, G. Crelle J. 41 (1851) 141-, 227-. 

Quarter squares, method of using table. 

Laundy, S. L. Assur. Mg. 9 (*1861) 112-. 
Report of Commission on tables. Mehmke, R. 

D. Mth. Vr. Jbr. 7 (1899) (Heft 1) 123-. 
Bhind papyrus. Mansion, . Brux. S. Sc. A. 

12 (1888) (Pt. 1) 44-. 
Sang's seven-figure logarithms. Ellis, A. J. 

I. Act. J. 17 (*1873) 298. 
. Glaisher, J. W. L. I. Act. J. 17 

(* 1873) 298-. 
. Tucker, R. I. Act. J. 17 (*1873) 

299-. 
Signs of trigonometrical lines. Henri, M. 

N. A. Mth. 7 (1848) 285-. 
Sine-integral, cosine-integral, exponential in- 
tegral. Glaisher, J. W. L. Phil. Trans. 160 

(1870) 367-. 
, tangent, etc. of small angles from 5 figure 

tables by using secants. Pfeil, L. von. Arch. 

Mth. Ps. 42 (1864) 305-. 
Sines, for use in plotting mines. La Chabeaus- 

siere, A. J. M. P. J. Mines 35 (1814) 321-. 
Smallest number of entries necessary in a 7 

figure log. table. Steggall, J. E. A. Edinb. 

Mth. S. P. 10 (1892) 35-. 
Squares and cubes. G., H. Nicholson J. 8 

(1804) 150- ; 9 (1804) 123-. 

. , calculation. O., E. Nicholson J. 9 

(1804) 4-, 171-. 

, (Jahn), errors. Kulik, J. P. Bohm. 

Gs. Ab. 2 (1843) (Sect. B. 1841) 19-. 
Sum or difference of two numbers whose logs. 

are given. Gauss, C. F. Zach M. Cor. 26 

(1812) 498-. 



Addresses, Lectures, etc. 0040 

Syzygies, irreducible, of quantics. Sylvester, 
J. J. Am. J. Mth. 4 (1881) 41-. 

Trigonometric functions of cyclic and hyper- 
bolic sectors. Gronau, J. F. M. [1863-65] 
Danzig Schr. 1 (1866) (Heft 1) viii + 151 pp. ; 



, history question. Prony, R. de. Par. Mm. 
de I'l. 5 (1802) (H.) 67-. 

, new system. Bouche, A. M.-et-L. Mm. S. 
Ac. 8 (1860) 145-. 

, note. Hill, C. J. D. Lund Phys. Sallsk. 
Ts. 1 (1838) 283-; Grunert Arch. 1 (1841) 
191-. 

Trigonometry and astronomy, fundamental 

tables. Sang, E. Edinb. B. S. P. 16 (1890) 

249-. 
Two old tables. Pendlebury, R. Mess. Mth. 

4 (1875) 8-. 
Values of A"0 m . Herschel, J. [attributed to 

Lacroix in (ra)]. N. A. Mth. 13 (1854) 272-. 

-- S fc =2ra-*. Stieltjes, T. J. Acta Mth. 

10 (1887) 1 299-. 
-- I .*. 4 ... (*- 1|/8 . 8 . 5 ... a>, denominators 

being primes. Glaisher, J. W. L. Mess. 

Mth. 28 (1899) 1-. 
Zonal harmonics. Perry, J. [1890] L. Ps. S. 

P. 11 (1892) 221- ; Ph. Mg. 32 (1891) 512-. 

0040 Addresses, Lectures, etc., of 
a general character. 

American Mathematical Society, past and 
future. McClintock, E. [1894] N. Y. Am. 
Mth. S. Bll. 1 (1895) 85-. 

Astronomy, geometry, and arithmetic, three 
discourses. Gamier, J. G. (vi Adds.) Gand 

A. Ac. (1817-18) 83 pp. 

Chicago, inaugural address, Aug. 21, 1893. 

Klein, F. N. Y. Mth. S. Bll. 3 (1894) 1-. 
Collaboration in mathematics. Greenhill, A. G. 

[1892] L. Mth. S. P. 24 (1893) 5-. 
Combinatory analysis: a review. MacMalum, 

P. A. [1896] L. Mth. S. P. 28 (1897) 5-. 
Confluences and bifurcations of certain theories. 

(Presidential address, 1888.) Cockle, (Sir) J. 

L. Mth. S. P. 20 (1889) 4-. 
' ' Deutsche Naturforscher, ' ' address at meeting, 

1858. Eisenlohr, W. Grunert Arch. 32 

(1859) 140-. 
Differential equations and applied mathematics, 

historical sketch. Naetsch, E. Civing. 41 

(1895) 655-. 
General considerations. Glaisher, J. W. L. 

B. A. Ep. (1890) 719-. 

Geometrical method. (Presidential address.) 
Larmor, J. Mth. Gz. 1 (1900) 1-. 

researches, comparative reflections on recent. 
Klein, F. A. Mt. 17 (1889-90) 307-. 

Geometry applied to practical life. Pearson, K. 

Nt. 43 (1891) 273-. 
Grassmann's " Ausdehnungslehre " applied to 

mechanics. Schlegel, V. Civing. 40 (1894) 

59-. 
Historiography of mathematics. Cantor, . 

[1900] N. Y. Am. Mth. S. Bll. 7 (1901) 



0040 Addresses, Lectures, etc. 

History of mathematics and physics. (Anniver- 
sary address.) Knibbs, G. H. N. S. W. E. 
S. J. 33 (1899) 1-. 

Influence of applied, on the progress of pure, 
mathematics. (Presidential address.) Walker, 
J. J. [1890] L. Mth. S. P. 22 (1891) 4-. 

Invariants of motion, and elementary geometry. 
Study, E. Leip. Mth. Ps. B. 48 (1896) 649-. 

Lectures at Ecole Normale. La, Place, P. S. 
(le marquis) de. Par. Se. EC. Norm. 1 
(1800) 16-, 268-, 381- ; (pte. 2) 3-, 130- ; 
2 (1800) 116-, 302- ; 3 (1800) 24-; 4 (1800) 
32-, 223-; 5 (1800) 201- ; 6 (1800) 32-. 

. Lagrange, J. L. de. Par. Se. 

EC. Norm. 1 (1800) (pte. 2) 3-, 34-; 3 (1800) 
227-, 276-, 463-; 4 (1800) 401- ; 10 (1801) 
5-. 

(elementary), 1795. Lagrange, 

J. L. de. Par. EC. Pol. J. 2 (1812) (7 e et 8 e 
call.) 173-. 

Mathematical problems. Hilbert, D. Gott. 
Nr. (1900) 253-. 

theories, etc. (Presidential address, 1883.) 
Cayley, A. B. A. Bp. (1883) 3-. 

tripos, the. (Presidential address.) Glaisher, 
J. W. L. L. Mth. S. P. 18 (1886-87) 4-. 

Mathematics. Kempe, A. B. [1894] L. Mth. 

S. P. 26 (1895) 5-. 
, influence on physical science. Bastarrica, 

J. Chile A. Un. (1852) 41-. 

and natural science, mutual relations. 
Wild, J. St Gal. B. (1885-86) 101-. 

Phys. Sect. Address, 1865. Spottiswoode, W. 
B. A. Kp. 35 (1865) (Sect.) 1-. 

, , 1869. Sylvester, J. J. B. A. 

Bp. 39 (1869) (Sect.) 1-. 

. , , 1870. Maxwett, J. C. B. A. Ep. 

40 (1870) (Sect.) 1-. 

, , 1871. Tait, P. G. B. A. Ep. 41 

(1871) (Sect.) 1-. 
,,1873. Smith, H. J. S. B.A.Ep. 

43 (1873) (Sect.) 1-. 
. , Presidential address, 1883. Henrici, 

0. M. F. E. B. A. Ep. (1883) 393-. 

, , 1897. Pure mathematics. 
Forsyth, A. E. B. A. Ep. (1897) 541-. 

Mission of science, address. Thurston, E. H. 

Am. As. P. (1884) 227-. 
Modern function theory, development. Krause, 

. Giving. 34 (1888) 639-. 
Moscow Math. Soc., Jubilee, address. Bugaev, 

N. V. [1894] Eec. Mth. (Moscou) 18 (1896) 

vi-. 
Presidential address, March 21st, 1900. 

Bugaev, N. V. Eec. Mth. (Moscou) 21 (1901) 

537. 
Purposes of Brit. Assn., and external aspects of 

mathematics. (Presidential address, 1878.) 

Spottiswoode, W. B. A. Ep. (1878) 1-. 
Eiemann's surfaces. Hypergeometric function. 

Differential equations. Theory of numbers. 

(Lectures.) Klein, F. [1891-96] Mth. A. 45 

(1894) 140- ; 46 (1895) 77-; 48 (1897) 562-. 
Secondary needs and opportunities of English 

mathematicians. (Presidential address.) 

Elliott, E. B. [1898] L. Mth. S. P. 30 

(1899) 5-. 



Pedagogy 0050 

Universities and technical schools, address. 
Klein, E. D. Mth. Vr. Jbr. 7 (1889) (Heft 1) 
39-. 

0050 Pedagogy. 

Actuarial competence, requisites. Sutton, W. 

I. Act. J. 16 (*1872) 434-. 
Actuaries, importance of mathematical studies. 

Sprague, T. B. I. Act. J. 18 (*1876) 403-. 
, mathematical education. Kiepert, L. D. 
Nf. Vh. (1894) (Th. 2, Hdlfte 1) 16-. 

, . Fehr, H. Ens. Mth. 1 

447-. 
Actuary, education. Porter, H. W. 

Mg. 4 (*1854) 108-. 
Algebra, the first chapter. Anon. Educ. 

Times 39 (1886) 326-. 
in schools. Heppel, G. Mth. Gz. No. 4 

(1895) 25-. 

, teaching, in 1676. (Henrion's "Euclid.") 
Mansion, . Brux. S. Sc. A. 19 (1895) 
(Ft. 1) 101-. 
American colleges, mathematics. Eddy, H. T. 

Am. As. P. (1884) 37-. 

Analytical geometry, combination of planimetry 
and stereometry in teaching. Eipert, L. 
As. Fr. C. E. (1900) (Pt. 2) 1036-. 
Application of mathematical and mechanical 
principles to technical problems. Heun, K. 
D. Mth. Vr. Jbr. 5 (1901) (Heft 1) 91-. 
Arithmetic and algebra, elementary teaching. 
Eecknagel, G. D. Nf. Vh. (1899) (Th. 2, 
Hdlfte 1) 279-. 
, the first stage. Quick, (Eev.) E. H. 

Educ. Times 41 (1888) 227-. 
, the five fundamental operations. Kupffer, 

K. Dorpat Sb. 10 (1895) 359-. 
, teaching. Edinb. Mth. S. Comm. Edinb. 

Mth. S. P. 6 (1888) 89-. 
, , method. Elowson, G. Ts. Mt. Fys. 2 

(1869) 40-. 
, , . Moesta, C. W. Chile A. Un. 

(1852) 322-. 

Arithmetical problems in secondary schools, 
treatment. Burali-Forti, C. Ev. Mt. 1 
(1891) 31-. 
Blind, teaching of the congenitally. Penjon, 

. Gergonne A. Mth. 3 (1812-13) 308-. 
Combination of solid with plane geometry in 
teaching. Candida, G. Ens. Mth. 1 (1899) 
204-. 

Descriptive geometry, first lesson. Budelot, G. 
Ens. Mth. 1 (1899) 286-. 

, lacuna in the teaching. Tilly, (Maj.) 

de. Brux. S. Sc. A. 9 (1885) (Pt. 2) 95-. 

Educational testimony concerning the calculus. 

Meech, L. W. Des Moines Anal. 1 (1874) 

133-. 

Elliptic functions, teaching of theory. Mansion, 

. Brux. S. Sc. A. 24 (1900) (Pt. 1) 54-. 
Equations, choice of examples in teaching. 
Breton \de Champ}, P. N. A. Mth. 2 (1843) 
539-. 
Errors in mathematical text books. Beyer, . 

Grunert Arch. 3 (1843) 113-. 
Euclid and teaching of geometry. Magnus, P. 
Educ. Times 33 ( 1880) 81-. 



30 



0050 Pedagogy 

Examination questions, composition. Laisant, 
C. A. Ens. Mth. 1 (1899) 120-. 

. , solutions. Sprague, T. B. Assur. Mg. 
10 (*1863) 45-; 13 (*1867) 253-; I. Act. J. 
14 (* 1869) 147-. 

, _ ( a correction). Adler, M. N. I. Act. 

J. 14 (*1869) 242. 
Examinations, judging in mathematical. 

Bordoni, A. [1841] Mil. Mm. I. Lomb. 1 

(1843) 189-. 
, problems suitable. Wittstein, T. Grunert 

Arch. 7 (1846) 27-. 
Exposition of pure mathematics. Delarue, 

D. M. (xn) [1869] Eec. Mth. (Moscou) 

4 (1869-70) (Ft. 2) 81-. 
Formulae, special application of mnemonics. 

Hoffmann, L. Forster Al. Bauztg. 10 (1845) 

362-. 
Geometrical drawing, teaching. Henrici, 0. 

B. A. Ep. (1895) 608. 

teaching, reform. Fiedler, W. Ziir. Vjschr. 
22 (1877) 82-. 

, . Wittek, H. D. Nf. Vh. (1894) 

(Th. 2, Hdlfte 1) 317-. 

Geometry and analysis, higher, Naples Uni- 
versity, 1870-71. Bernardinis, G. de, <& 

Fuortes, T. G. Mt. 9 (1871) 233-. 
, elementary, new trend in. Ciamberlini, C. 

Ev. Sc.-Ind. 30 (1898) 99-, 113-, 153-. 
, , teaching. Develey, . Bb. Un. 8 

(1818) 257-. 
, , . Barclay, A. J. G. Edinb. Mth. 

S. P. 2 (1884) 24-. 
, , . Diekmann, . D. Nf. Tbl. (1888) 

342-. 
, experiment in teaching. Fraser, A. Y. 

Edinb. Mth. S. P. 5 (1887) 94-. 
, first teaching. Laisant, C. A. Ens. Mth. 

1 (1899) 339-. 
, higher, teaching. Chasles, M. Liouv. J. 

Mth. 12 (1847) 1-. 
, natural. Mault, A. Tasm. E. S. P. 

(1886) 103-. 
, practical, development. (Graphics.) Anon. 

Elect. 28 (1892) 298-. 
, , . ( .) Thompson, S. P. Elect. 28 

(1892) 332-. 
, solid, teaching in higher schools. 

Hildebrandt, C. D. Nf. Vh. (1897) (Th. 2, 

Halfte 1) 34-. 
, , at Strassburg. Krazer, A. D. 

Mth. Vr. Jbr. 8 (1900) (Heft 1) 119-. 

in schools. Heppel, G. Edue. Times 50 
(1897) 181-. 

, teaching. Dallas, E. J. Nt. 59 (1898- 

99) 416. 
, . Eeinhardt, N. V. Kazan S. Ps.-Mth. 

Bll. 8 (1899) (Prot.) 19-. 

versus Euclid. Minchin, G. M. Nt. 59 
(1898-99) 369-. 

Graduated system of teaching, especially in 

geometry. Bazala, J. D. Nf. Vh. (1894) 

(Th. 2, Hdlfte 1) 313-. 
Higher mathematics at Italian Universities, 

teaching. Pascal, E. Ev. Mt. 3 (1893) 

170-. 
Hyperbolic functions in teaching. Barbarin, 

P. Ens. Mth. 2 (1900) 443-. 

31 



Pedagogy 0050 

Imaginaries, treatment in higher school 

teaching. Pietzker, F. [1898] D. Mth. Vr. 

Jbr. 7 (1899) (Heft 1) 154-. 
Indices and surds, teaching. Genese, E. W 

Mth. Gz. 1 (1900) 339-. 
Infinitesimal calculus, course. Obrecht, A. 

Santiago de Chile Un. A. 87 (1894) 533-, 

657-, 715- ; 88 (1894) 39-; 90 (1895) 45-; 

91 (1895) 677-; 93 (1896) 105-, 241- ; 103 

(1899) 699-, 887-; 104 (1899) 39-, 201-, 

359-, 747-, 1061- ; 106 (1900) 79-, 375-, 

545-, 949-, 1097-. 
Infinity in elementary mathematics. Lamarle, 

E. [1851] Brux. Ac. Sc. Mm. 27 (1853) 31 pp. 
Inverted problems (an old arithmetic book). 

C., H. A. Educ. Times 48 (1895) 29-. 
Languages and mathematics in state schools 

of modern Germany. Baumann, H. Educ. 

Times 37 (1884) 98-. 
Leibnitz, calculus of, and its teaching. 

Arnoux, E. As. Fr. C. E. (1900) (Pt. 2) 

1089-. 
Mathematical history, 8 years of teaching. 

Favaro, A. Bb. Mth. (1887) 49-. 

, lectures in Moscow University, pro- 
gramme of course. Bobynin, V. V. Fschr. 
Mth. (1890) 87; Bb. Mth. (1891) 79-. 

at Munich. Steinschneider, M. Bb. 

Mth. (1897) 113-. 
, university course. Enestrom, G. Bb. 

Mth. (1890) 1-. 
instruction in France. Pierpont, J. N. Y. 

Am. Mth. S. Bll. 6 (1900) 225-. 

problems, and the development of mathe- 
matics. Hilbert, D. Ens. Mth. 2 (1900) 
349-. 

teaching. Hudson, W. H. H. Educ. 
Times 46 (1893) 135-. 

. Biraben, F. Arg. S. Ci. A. 48 (1899) 

106-, 156-. 

. Duclaux, E. Ev. Sc. 11 (1899) 353-. 

. Garciade Galdeano, Z. As. Fr. C. E. 

(1900) (Pt. 2) 1052-. 

. Perry, J. Nt. 62 (1900) 317-. 

. Heaviside, O. Nt. 62 (1900) 548-. 

, changes. Piola, G. (vm) [1840] Bb. 

It. 2 (1841) 159-. 
, curiosities in early English. Heppel, 

G. Educ. Times 38 (1885) 145-. 
, elementary. Laisant, . Ev. Sc. 11 

(1899) 358-. 
, general principles. Galdeano, Z. G. de. 

Ens. Mth. 1 (1899) 195-. 
at German Universities, especially 

Gottingen. Fano, G. Ev. Mt. 4 (1894) 

170-. 
in Germany, history. Giinther, S. Ens. 

Mth. 2 (1900) 237-. 

in higher grade schools (gymnasiums 
and lyceums). Catania, S. Ev. Mt. 5 
(1895) 33-. 

Holland. Cardinaal, J. Ens. Mth. 

2 (1900) 317-. 
, methods. Grunert, J. A. Arch. Mth. 

Ps. 42 (1864) 348-. 

in preparation for the " Ecole Poly- 
technique." Laurent, H. Ens. Mth. 1 

38-. 



0050 Pedagogy 

Mathematical teaching, reform. Mair, D. 

Nt. 62 (1900) 389. 

, . Woollen, H. Nt. 62 (1900) 436. 

, . Beard, W. F. Nt. 62 (1900) 466. 

, . Stromeyer, C. E. Nt. 62 (1900) 523. 

in Eussia. Bobynin, V. V. Ens. Mth. 

1 (1899) 420-. 
, history. Bobynin, V. V. Ens. 

Mth. 1 (1899) 77-. 
schools. Lie, S. Christiania F. 

(1884) No. 16, 8pp.; (1885) No. 11, 10 pp. 
. Tafelmacher, A. Santiago de 

Chile Un. A. 85 (1893) 35-. 
, simplification of elementary. Heppel, 

G. Educ. Times 44 (1891) 463-. 
in United States. Safford, T. H. N. Y. 

Mth. S. Bll. 3 (1894) 4-. 

universities in 1894. Galdeano, 
Z. G. de. Fschr. Mth. (1893-94) 118. 

, problems and methods. Klein, 

F. D. Mth. Vr. Jbr. 7 (1899) (Heft 1) 126-. 
, use of history. Heppel, G. Nt. 48 

(1893) 16-. 
, practical applications. Bettazzi, 

E. Ens. Mth. 2 (1900) 14-. 
Mathematics for astronomy and navigation. 

Wilson, T. Mth. Gz. No. 4 (1895) 27-. 

at certain German Universities. Dillner, 

G. Ups. Arsk. (1876) 37 pp. 

, elementary, economy of thought. Meyer, 
W. F. D. Mth. Vr. Jbr. 7 (1899) (Heft 1) 
147-. 

in girls' schools. Bryant, (Mrs.) . Educ. 
Times 31 (*1878) 145-. 

, how to study. Degen, C. F. Kiob. Dn. 

Yd. Selsk. Skr. 2 (1801-2) 75-. 
, relations between university and high 

school in domain of. Schotten, H. D. Nf. 

Vh. (1898) (Th. 2, Halfte 1) 20-. 

in Eussia, history of study. Bobynin, V. 
Bb. Mth. (1888) 103-. 

schools. Heppel, G. Educ. Times 39 

(1886) 385-. 

as a scientific and pedagogic aid. Bugaev, 
N. V. (xn) [1869] Eec. Mth. (Moscou) 3 
(1868) (Pt. 2) 183-. 

in Spain. Galdeano, Z. G. de. Ens. Mth. 
1 (1899) 6-. 

in 1893-94. Galdeano, Z. G. de. 

Fschr. Mth. (1893-94) 117. 

teaching of physics, importance. 
Calzecchi, T. Ev. Sc.-Ind. 30 (1898) 65-. 

Mensuration, note. Lefevre, A. Texas Ac. 

Sc. T. 2 (No, 2) (1899) 39-. 
Multiplication, method of performing. Berdelle, 

C. As. Fr. C. E. (1884) (Pt. 2) 584-. 
Notion of the infinite in teaching elementary 

geometry. Eipert, L. Ens. Mth. 2 (1900) 

127-. 
. (Correction of error 

in Eipert's paper, p. 129.) Niewenqlowski, 

B. Ens. Mth. 2 (1900) 219. 

a limit in teaching. Clasen, . 
Braunschw. Vr. Nt. Jbr. (11) (1899) 159-. 

on number and limit in teaching. Prinqs- 
heim, A. D. Mth. Vr. Jbr. 6 (1899) (Heft 
1) 73-. 



Institutions 0060 

Problem solving as a discipline. Hall, A. 

Wash. Ph. S. Bll. 11 (1892) 598-. 
Pure mathematics for engineering students. 

Hathaway, A. S. [1900] N. Y. Am. Mth. S. 

Bll. 7 (1901) 266-. 
Quadratic equation, theory. Macfarlane, A. 

Ens. Mth. 2 (1900) 363-. 

equations, solution. Mathews, G. B. Nt. 
57 (1897-98) 463-. 

Seducing results of measurement. Rndel, K. 

D. Nf. Vh. (1893) (Th. 2, Halfte 1) 217-. 
Eole of mathematics in general education. 

Budelot, G. Ens. Mth. 1 (1899) 222. 
Eules of multiplication, their nature and 

teaching. Baron, B. Ens. Mth. 1 (1899) 

317-. 
Scientific method in teaching. Binet, A. 

Ens. Mth. 1 (1899) 29-. 
Smith's-Prize papers. Cayley, A. Mess. 

Mth. 3 (1874) 165- ; 4 (1875) 6- ; 6 (1877) 

173-. 
Statutes for testing teachers, and Mathematical 

course. Hauck, G. D. Nf. Vh. (1899) (Th. 

2, Halfte 1) 17-. 
. (Prussian.) Weber, H. D. Nf. 

Vh. (1899) (Th. 2, Halfte 1) 9-. 
. ( .) Scliotten, H. D. Nf . Vh. 

(1899) (Th. 2, Halfte 1) 26-. 
Statutory tests for teachers in Bavaria. Eudel, 

K. D. Nf. Vh. (1899) (Th. 2, Halfte 1) 29-. 
Synthetic and projective geometry, need of, in 

analytical geometry. Davidescu, D. A. 

Bucarest S. Sc. Bll. (1900) 19-. 
Systematisation of mathematics. Ellis, A. J. 

E. S. P. 10 (1859-60) 85-. 

Technical High Schools in America. Engels, H. 
Giving. 40 (1894) 13-. 

instruction, especially its geometry. 
Paganini, C. Mil. G. I. Lomb. 1 (1841) 
291-. 

teaching in Chili. Nogues, A. F. [1893- 
94] Santiago de Chile Un. A. 85 (1893) 
277-, 345-, 515-. 

Training of teachers of science in higher 

schools, in view of modern requirements. 

Schwalbe, B. D. Nf. Vh. (1896) (Th. 2, 

Halfte 1) 15-. 
Trigonometry, teaching. Aragon,A. Mex. S. 

"Alzate" Mm. 5 (1891) 69-. 
, of elements. Fehr, H. Ens. Mth. 1 

(1899) 45-. 
'Unitary' method in teaching proportion. 

Beta. Educ. Times 32 (*1879) 259-. 
Universities and technical schools, address. 

Klein, F. D. Mth. Vr. Jbr. 7 (1899) (Heft 

1) 39-. 
University lectures on infinitesimal calculus. 

Pringsheim, A. D. Mth. Vr. Jbr. 7 (1899) 

(Heft 1) 138-. 
Vector theory, teaching. Fontene, G. Ens. 

Mth. 1 (1899) 50-. 



0060 Institutions. 

Franklin Institute during 75 years. Thurston, 
E. H. Franklin I. J. 149 (1900) 81-. 



32 



0070 Nomenclature 



0070 Nomenclature. 

"Al-djebr," exact meaning of word. Vaux, 

C. de. Bb. Mth. (1897) 1-. 
Algorithm, meaning of term. Hunrath, K. 

Bb. Mth. (1887) 70. 
Antiparallels. Langley, E. M. Nt. 40 (1889) 

460-. 
"Autotomic" curves. Basset, A. B. Nt. 62 

(1900) 572. 
. Orchard, H. L. [1900] Nt. 63 (1900- 

01)7. 
. Thorn, A. S. [1900] Nt. 63 (1900- 

01) 7. 
. Basset, A. B. [1900] Nt. 63 (1900- 

01) 82. 
Chinese arithmetical notation. Edkins, . 

Nt. 37 (1888) 65. 
"Conjugate angles," new geometrical term. 

Worthington, A. M. Nt. 47 (1892-93) 8. 
Cuneiform numerical signs, transmission. 

Bobynin, V. Bb. Mth. (1893) 18-. 
Curves without double points. Richmond, H. 

[1900] Nt. 63 (1900-01) 58. 
Decimal division of circle (i.e. of right angle). 

Hatzfeld, A. Bv. Sc. 48 (1891) 655-. 
Determinant notation. Nan-son, E. J. Ph. 

Mg. 44 (1897) 396-. 
Differential notation and teaching. Poincare, 

H. Ens. Mth. 1 (1899) 106-. 
Duodecimal system. Heaviside, 0. Elect. 37 

(1896) 489. 
Functions, growth of notation for. Enestrom, 

G. Bb. Mth. (1891) 89-. 
General and logico-mathematical notation. 

Oliver, J. E. A. Mth. 4 (1888) 186-. 
Geometrical square, nomenclature. Weissen- 

born, H. Bb. Mth. (1888) 37. 
Geometrography or systematic notation for 

geometric constructions. Lemoine, E. G. 

Teix. J. Sc. 12 (1895) 114-. 
Gnomon theorem (Euc. I. 43). Allman, G. J. 

Bb. Mth. (1887) 22. 
Kardaga. Steinschneider,M. Bb. Mth. (1891) 

114. 
Language, mathematical and scientific. Anon. 

(vi 543). Gergonne A. Mth. 12 (1821-22) 

322-. 
Logarithms, notation. Draenert, . D. Nf. 

Tbl. (*1876) (Suppl.) 173-. 
Nomenclature. Dantas Pereira, J. M. Lisb. 

Mm. Ac. Sc. 10 (1830) (pte. 2) 197-. 
, geometrical. Fontene, G. Ens. Mth. 2 

(1900) 134- . 
of metric system. Rautenfeld-Lindenruh, 

H. von. Eiga Cor.-Bl. 38 (1895) 85. 
Notation. Lubbock, J. W. [1829] As. S. 

Mm. 4 (1831) 471-. 

. Sylvester, J. J. Ph. Mg. 7 (1854) 50-. 
. Houzeau, J. C. Brux. Ac. Bll. 39 (1875) 

487-. 
, algebraic. Jarrett, T. [1827] Camb. Ph. 

S. T. 3 (1830) 65-. 
, . Cottins, J. V. Science 20 (1892) 

359. 



Nomenclature 0070 

Notation, arithmetical. McColl, H. Educ. 

Times 33 (*1880) 111. 
, calculus. Couto, M. V. do, & Simoes 

Margiochi, F. Lisb. Mm. Ac. Sc. 3 (pte. 2) 

(1814) 48-. 

of decimal fractions. Gravelaar, N.L.W.A. 
N. Arch. Wisk. 4 (1899) 54-; Fschr. Mth. 
(1899) 37. 

, numerical. Prevost, P. Bb. Un. 3 (1816) 

306- . 
, questions concerning. Eipert, L. Ens. 

Mth. 1 (1899) 139. 

useful in analysis. Ocagne, M. d\ Par. S. 
Mth. Bll. 15 (1887) 156-. 

TT to denote 3-14159..., first use. Enestrom, G. 

Bb. Mth. (1889) 28. 
, . Ball, W. W. E. Bb. 

Mth. (1894) 106. 
Printing mathematical symbols. Mitchell, 

C. T., and others. Elect. 29 (1892) 652,, 

et seq. 
. Thompson, S. P. Nt. 46 (1892) 

513. 

mathematics. Cassie, W. [1892] Nt. 47 
(1892-93) 8-. 

. Jackson, M. J. Nt. 47 (1892-93) 227. 

Quantitative comparisons, a common error in 

speech. Johnson, G. H. Science 22 (1893) 

352. 
Eoulettes. Willson, F. N. Am. As. P. (1887) 

59-. 
Signs (for functions, operations, &G.). Hoppe, 

R. Arch. Mth. Ps. 61 (1877) 323-. 
Spoken numeration, from international point 

of view. Berdelle, C. Ens. Mth. 1 (1899) 

269-. 
Symbols. Hall, A. [1889] A. Mth. 5 (1889- 

90) 19. 

of non-existence. Doolittle, M. H. Wash. 
Ph. S. Bll. 11 (1892) 603. 

Terminology. Laisant, C. A. Ens. Mth. 1 
(1899) 22-. 

and conceptions. Gyory, S. (xn) Mag. 
Tud. Ak. Ets. 3 (No. 12) (1869) 131-. 

, mathematical. Roberts, S. [1882] L. 

Mth. S. P. 14 (1882-83) 5-. 
, suggestions. Muirhead, R. F. Edinb. 

Mth. S. P. 13 (1895) 143. 
Trigonometry, development of notation. Braun- 

milhl, A. von. Bb. Mth. 1 (1900) 64-. 
Umbral notation. Harley, (Rev.) R. B. A. 

Up. (1887) 600-. 

Uniform notation for mathematical and physi- 
cal quantities. Winkler, E., t& Keck, . 

Giving. 30 (1884) 285-. 
. Keck, . Hann. Archt.- 

Vr. Z. 30 (1884) 285-. 
Use of + and to denote ' ' plus ' ' and ' ' minus. ' ' 

Enestrom, G. Stockh. Ofv. (1894) 243-; 

Fschr. Mth. (1893-94) 59-; Bb. Mth. (1899> 

105-. 
terms "square" and "cube" in Algebra. 

Taylor, W. B. Wash. Ph. S. Bll. 11 (1892V 

590-. 
Variation, variable, &c., remarks on the words. 

Strauch, G. W. Grunert Arch. 7 (1846) 

221-. 



33 



0080 Instruments 

0080 Instruments, including 
Calculating Machines. Models. 

INSTEUMENTS. 

Algebraical machines. Torres, L. As. Fr. C. 

R. (1895) (Pt. 2) 90-. 
Angle, correction for tilt of horizontal circle. 

Matzka, W. Grunert Arch. 13 (1849) 113-. 
, instrument for dividing into equal parts. 

Gouin, E. Les Mondes 12 (1866) 470-. 

measurer. Heineken, N. J. Intell. Obs. 8 

(1886) 197-. 

for schools. Fischer, F. W. [1876] 

Arch. Mth. Ps. 61 (1877) 99-. 
, mechanical division. Perrin, E. [1875] 

Par. S. Mth. Bll. 4 (1876) 85-. 
_, . Brocard, H. [1876] Par. S. Mth. 

Bll. 5 (1877) 43-. 
Antigraph, a reversing drawing instrument. 

Marcus, S. Wien SB. 17 (1855) 282-. 
Arcs, instrument for drawing. Alderson, Jas. 

Gill Tech. Hep. 10 (1829) 128-. 
Area, moment of inertia, and centre of gravity 

of a plane area, apparatus for giving. Col- 

lignon, E. (ix) A. Pon. Chauss. 3 (1872) 

223-. 
Arithmoplanimeter. Lalanne, L. Par. A. Pon. 

Chauss. 20 (1840) 3-. 

Axonometric drawing, protractors for, prepara- 
tion. Anon, (vi 316) Giving. 7 (1861) 83-. 
Besson, Jacques, (t!569), (Mathematical in- 
struments). Beck, T. Giving. 36 (1890) 

191-. 
Calculating machine. Cunq's "machine a 

debits," for calculating quantity of water 

flowing through an orifice. Sornin, J. Toul. 

Mm. Ac. 6 (1856) 346-. 
Calculimeter (sort of slide rule). Fenton, J. J. 

Viet. B. S. P. 2 (1890) 84-. 
Chinese abacus or souan-pan. Rodet, L. Par. 

S. Mth. Bll. 8 (1880) 158-. 
Circles, instrument for dividing on paper. 

Balfour, J. M. (vi Adds.) [1859] Edinb. T. 

Sc. S. Arts 5 (1861) 149-. 

with remote centres, construction. Fischer, 
E. Dingier 294 (1894) 133-. 

Circular arcs, instrument for use of mechani- 
cians for comparison of. Sipos, P. (vi Adds.) . 
Berl. Sm. D. Ab. 2 (1796) 201-. 

Compass, bicentric. Maze (I'abbe) C. Les 
Mondes 8 (1884) 703-. 

for drawing spirals. Hartung, A. Dingier 
266 (1887) 12-. 

, elliptic, new. Jost, K. Wien Ak. Sb. 95 

(1887) (Ab. 2) 251-. 

, hyperbolic. Eeichelt, K. F. Cztg. Opt. 
17 (1896) 208. 

Compasses, copying , a simple form of panto- 
graph. Sedlaczek, J. Wien SB. 16 (1855) 
180-. 

, elliptic. Burchard, L. Carl Bpm. 13 
(1877) 528-. 

, improvement. Mollinger, 0. Sch. Gs. 
Vh. (1850) 52-. 

, proportional. Narrien, J. Thomson A 
Ph. 8 (1816) 338-. 



Instruments 0080 

Compasses, proportional. Butkevlch, F. S. (xn) 

[1873] Mosc. S. Sc. Bll. 39 (No. 2) (1880) 

128-. 
_, _. Palacios, D. Mex. S. " Alzate " Mm. 

7 (1893) 193-. 
, trisecting, Laisant. Brocard, H. Par. S. 

Mth. Bll. 3 (1875) 47-. 
Conic section compass. Meyn, R. Giving. 8 

(1862) 247-. 
compasses. Frizell, J. P. Camb. (M.) 

Mth. M. 1 (1859) 262-. 
, Drzewiecki's for direct construction 

of conies with mathematical pen. Kuhn, M. 

Carl Bpm. 10 (1874) 420-. 

sections, instrumentfor drawing. Rebicek, G. 
Carl Bpm. 11 (1875] 64-. 

Curve description; kinograph. Engelmeier, 
P. K. [1886-89] Mosc. S. Sc. Bll. 65 (No. 1) 
(1890) 89-. 

for drawing curves (elastic lamina) ' ' tira- 
curve-opisometer." Rossi Re, V. de. Bm. 
N. Line. At. 33 (1880) 232-. 

tracer. Pirani, E. Arch. Mth. Ps. 1 (1884) 
113-. 

and root finder. Bashforth, F. B. A. 

Bp. (1845) (pt. 2) 3-. 

tracing apparatus. Cayley, A. L. Mth. S. 
P. 4 (1871-73) 345-. 

, designing of apparatus for. TJiallmayer, 

V. Carl Bpm. 14 (1878) 713-. 
machine. Dechevrens, M. C. B. 130 

(1900) 1616- . 
, mechanical. Jessop, C. M. QJ. Mth. 

22 (1887) 151-. 
Curves described by Jopling's apparatus, nature. 

Tredgold, T. Tilloch Ph. Mg. 62 (1823) 211-. 
, mechanical description. Russell, W. H. L. 

[1869] B. S. P. 18 (1870) 72-. 
Curvimeter (for finding length of curves). 

Crane, W. R. Kan. Un. Q. 4 (1896) 121-. 
Cycloids, description. Kracht,H. Dingier 289 

(1893) 108-. 
Descriptive geometry, apparatus for illustrating. 

Hoza, F. Arch. Mth. Ps. 53 (1871) 188-. 
, teaching. Weissand, . N. A. 

Mth. 14 (1855) 47-. 
Diagonal scale principle applied to angular 

measurement in circular slide-rule. Campbell, 

J. R. L. Mth. S. P. 6 (1875) 73-. 
Diagrammometer, cypher. Kozlov, V. S. Bs. 

Ps.-C. S. J. 23 (Ps.) (1891) 180- ; C. E. Ill 

(1890) 166-. 
Difference engine, new. Grant, G. B. Am. 

J. Sc. 2 (1871) 113-. 
Division of angles and arcs of circles. Murphy, 

I. J. Belfast NH. S. Ep. & P. (1892-93) 47-. 
straight line into equal parts, machine 

for. Soave, F. Verona Mm. S. It. 8 (1799) 

56-. 
toothed wheels, machine for. Glasser, 

A. von. Dingier 252 (1884) 56-. 
Drawing instruments, especially ellipsographs 

in theory and practice. Fischer, E. Dingier 

255 (1885) 188-, 217-, 261-. 
Egg-oval, perfect, machine for drawing ; and 

advantageous method of producing curvilineal 

figures. Hay, D. R. Edinb. N. Ph. J. 40 

(1846) 331-. 



34 



0080 Instruments 

Ellipses, paradox in tracing. Lametz, . Metz 

Ac. Mm. 79 (1900) 69-. 
Ellipsograph. Leninn, M. St Pet. Ac. Sc. 

Bll. 5 (1839) 377-. 
. Thallmayer, V. Dingier 226 (1877) 237-; 

227 (1878) 337-. 
. Sidersky, D. Arch. Mth. Ps. 65 (1880) 

420- . 
. Hendricks, J. E. Des Moines Anal. 10 

(1883) 161-. 
. Grant, G. B. Franklin I. J. 122 (1886) 

301. 

. Schromm, F. Z. Instk. 12 (1892) 139-. 
. Delone, N. Mosc. S. Sc. Bll. 83 (No. 2) 

(1894) 11-; Fschr. Ps. (1895) (Ab. 1) 351. 
. Riefler, C. Z. Instk. 16 (1896) 115-. 

of Proclus. Blake, E. M. [1898] Am. J. 
Mth. 22 (1900) 146-. 

and protractor. Burnliam, S. W. Pop. As. 
4 (1897) 181-, 336. 

Ellipsographs. Zistl, M. Cztg. Opt. 5 (1884) 

245-, 258-, 265-. 

. Hartmann, W. Z. Instk. 11 (1891) 285-. 
Ellipsometer. Henry, F. (x) A. Pon. Chauss. 

3 (1872) 459-. 

. Jannettaz, E. Fr. S. Mn. Bll. 15 (1892) 

237- ; 16 (1893) 205-. 
Elliptographs, and a mechanical rocker for 

detecting oscillations. Alexander, T., & 

Thomson, A. W. Ir. Ac. T. 29 (1887-92) 

673-. 
Epi- and hypo-cycloids, apparatus for tracing. 

Thallmayer, V. Dingier 228 (1878) 312-. 
Equations, apparatus for graphic solution. 

Lill, E. Les Mondes 16 (1868) 325-. 

of form \ n + aA 2 + 6X + c = 0, Mehmke's ap- 
paratus for solution. Mlodzeevskij, B. K. 
Mosc. S. Sc. Bll. 92 (No. 1) (1896) 36-; 
Fschr. Mth. (1896) 72. 

with imaginary roots, apparatus for graphic 
solution. Lill, E. N. A. Mth. 7 (1868) 
363-. 

, machine for solution. Girard, P. van. 

Wien Jb. Pol. I. 14 (1829) 62-. 
, . Bashforth, F. B. A. Ep. (1845) 

(pt. 2) 3-. 
, . Boys, C. V. L. Ps. S. P. 7 

(1886) 355-; Ph. Mg. 21 (1886) 241-. 
, . Cunynglwme, H. L. Ps. S. P. 

7 (1886) 360- ; Ph. Mg. 21 (1886) 260-. 
, . Ocagne, M. d'. J. de Ps. 5 

(1896) 310-. 
, . Meslin, G. C. B. 130 (1900) 

888-. 
, of linear. Veltmann, W. Z. Instk. 

4 (1884) 338-. 

, simultaneous linear. Thomson, 

(Sir) W. (Lord Kelvin). [1878] B. S. P. 28 
(1879) 111-. 

, transcendental. Herschel (Sir) 

J.F. W. [1832] Camb.Ph. S. T. 4 (1833) 425-. 

, mechanical solution. Kempe, A. B. [1872] 
Mess. Mth. 2 (1873) 51-. 

, . Guarducci, F. Bm. K. Ac. Line. 

Mm. 7 (1891) 219-. 

, 3rd order, mechanical solution by a quadri- 
lateral linkage. Greenhill,A.G. Mess. Mth. 

5 (1876) 162-. 



Instruments 0080 

Equations, 3rd order, solution by slide-rule. 

Bour, E. [J. E. E.] C. E. 44 (1857) 22-. 
, 4th and 5th orders, solution by moving 

mechanisms. Ameseder, A. Wien Ak. Sb. 

93 (1886) (Ab. 2) 380- . 

to 7th order, machine for solution. Lalanne, 
L. C. E. 11 (1840) 859-. 

, (Lalanne). Cauchy, A. L. 

G. E. 11 (1840) 959-. 
Generation of orthogonal projections of plane 

curves, mechanical. Delaunay, N. Z. Mth. 

Ps. 40 (1895) 242-. 
Genesis of quantity demonstrated by means of 

two mechanical instruments. Araldi, (Capi- 

tano) A. (vn) [1828] Mod. Mm. Ac. Sc. 1 

(1858) (pte. 4) 90-. 
Geometrical drawing, apparatus for. Zmurko, 

W. [L.] (xn) Kosmos (Lw.) 5 (1880) 44-. 
Geometrography applied to different solutions 

of a problem. Lemoine, E. Par. S. Mth. 

Bll. 20 (1892) 132-. 
Harmonic analyser. Henrici, 0. [1894] L. Ps. 

S. P. 13 (1895) 77-; Ph. Mg. 38 (1894) 110-. 

. LeConte, J. N. Ps. Ev. 7 (1898) 27-. 

. Michelson, A. A. <& Stratton, S. W. 

Am. J. Sc. 5 (1898) 1-. 
for graphic determination of coefficients 

in Fourier series. Bervy, N. Mosc. Obs. 

A. 3 (Pt. 2) (1896) 109-. 

, Henrici and. Coradi's. Grabowski, L. 
Wiad. Mt. 4 (1900) 236-. 

, reading amplitude and epoch directly. 
Sharp, A . [1894] L. Ps. S. P. 13 (1895) 89- ; 
Ph. Mg. 38 (1894) 121-. 



, remarks on Henrici's. Perry, J. 

L. Ps. S. P. 13 (1895) 97- ; Ph. Mg. 38 (1894) 

125-. 
, simple form. Yule, G. U. L. Ps. S. P. 

13 (1895) 403- ; Ph. Mg. 39 (1895) 367-. 
Helical epicycloids, instrument for describing. 

Burnaby, S. B. Amt. Mch. S. J. 3 (1879) 

115-, 160-, 194-, 228-. 
Herpolhode of Poinsot, and an apparatus of 

Darboux and Koenigs. Gilbert, P. Brux. 

S. Sc. A. 14 (1890) (Pt. 2) 25-. 
Hydraulic integration of differential equations. 

Petrovitch, M. Am. J. Mth. 20 (1898) 293-. 
Hyperbolas, apparatus for drawing. Thall- 
mayer, V. Dingier 228 (1878) 106-. 
, method of drawing. Burch, G. J. Ph. 

Mg. 41 (1896) 72-. 
, , Burch's. Wadsworth, F. L. 0. 

Ph. Mg. 41 (1896) 372-. 
Hyperbolograph. Cunynghame, H. [1886] L. 

Ps. S. P. 8 (1887) 67-; Ph. Mg. 22 (1886) 

138-. 

Instruments for ovals and for drawing in per- 
spective. B., R. Nicholson J. 9 (1804) 122-. 
Integral of product of 2 given functions, instru- 
ment for calculating. Thomson, (Sir) W. 

(Lord Kelvin). E. S. P. 24 (1876) 266-. 
Integraph, new. Barker, A. H. Sc. Abs. 1 

(1898) 381. 
Integrating differential equations of first order, 

Petrovich's apparatus. Price, W. A. Ph. 

Mg. 49 (1900) 487-. 
Integration, mechanical. Abdank-Abakanowicz, 

B. C. E. 94 (1882) 783-. 

35 02 



0080 Instruments 

Integration, mechanical. Nehls, C. Giving. 

20 (1874) 71- ; 21 (1875) 131-, 199-, 261-. 
, , applied to three bodies' problem. Strom- 

gren, E. Stockh. Ofv. (1900) 443-. 
, , of general linear differential equation of 

any order with variable coefficients. Thomson, 

(Sir) W. (Lord Kelvin). E. S. P. 24 (1876) 

271-. 
, , linear differential equations of 2nd 

order with variable coefficients. Thomson, 

(Sir) W. (Lord Kelvin). E. S. P. 24 (1876) 

269-. 

, , the product of two functions. Suther- 
land, W. Ph. Mg. 20 (1885) 175- ; 21 (1886) 

141-. 
Integrator, Amsler's. Nehls, C. Hann. Z. 

Archt. Vr. 18 (1872) 534-. 
. Abakanowicz,B. (xn) Krk. Ak. (Mt.-Prz.) 

Bz. & Sp. 7 (1880) 75-. 
, cubical, description. McElroy, G. W. A. 

Mth. 3 (1887) 105-. 
, disk-globe-and-cylinder. Thomson, (Prof.) 

Jas. E. S. P. 24 (1876) 262-. 
, instrument for graphic integration. Abdank- 

Abakanowicz, B. C. E. 92 (1881) 402-, 515-. 
, mechanical, Amsler-Laffon's. Merrifield, 

C. W. Nv. Archt. T. 21 (1880) 252-. 
, , for areas, etc. Deprez, M. C. E. 73 

(1871) 785-; Les Mondes 27 (1872) 10-. 
, -, ((Xdx+Ydy). Cayley, A. B. A. 

Ep. (1877) (Sect.) 18-. 
, , work done by a force. Fuchs, K. 

Mth. Termt. Ets. 13 (1895) 239-; Mth. Nt. 

B. Ung. 13 (1897) 144-. 

, new form. Marinovitch, B. Lum. Elect. 

17 (1885] 529-. 
, model. Napoli, D. & Abdank-Abakano- 

wicz, . C. E. 101 (1885) 592-. 
, Zmurko's. Skibinski,P.K. Kosmos(Lw.) 

9 (1884) 185- ; Wierf Ak. D. 53 (1887) (Ab. 2) 

35-. 
Integrators. Hummel, . Dingier 275 (1890) 

17-. 
, mechanical. Abdank-Abakanowicz, B. 

Lum. Elect. 18 (1885) 49-, 110-, 161-, 249-, 

306-, 393-, 535-, 589-; 24 (1887) 3-, 54-, 

161-. 
, two mechanical. Fraser, A. Y. Edinb. 

Mth. S. P. 4 (1886) 29-. 
Integrometer, new. Abdank-Abakanowicz, B. 

C. E. 95 (1882) 1047-. 

Involution and evolution of numbers, instru- 
ment for. Roget, P. M. [1814] Phil. Trans. 
(1815) 8-. 

Least squares, instrument for. Bouniakowsky , 
V. Pogg. A. 107 (1859) 463-. 

Linear differential equation of 2nd order, general 
mechanism for integrating. Tait, P. G. 
[1876] Edinb. E. S. P. 9 (1878) 118-. 

Link-work apparatus for describing curves. 
Janse, L. N. Arch. Wisk. 9 (*1882) 61-. 

Linkages for tracing conic sections. Stronq, 
W. M. A. Mth. 8 (1893-94) 181-. 

x m . Freeland, F. T. [18791 Am. J Mth 

3 (1880) 316-. 

Logical machine, Jevons' . Sonnenschein, E. A 
(xi) [1883] Birm. Ph. S. P. 4 (1885) 72-. 

36 



Instruments 0080 

Logical machine, new. Marquand, A. Am. 

Ac. P. 21 (1886) 303-. 

Mathematical instruments, models etc., ex- 
hibition in Munich. Dyck, W. D. Mth. Vr. 

Jbr. 3 (1894) 39-. 
Mechanisms, new: projector, ellipsograph, . . . 

Delaunay, N. Bll. Sc. Mth. 19 (1895) 240-. 
Mensurator and coelometer. Adams, M. L. 

Mth. S. P. 5 (1874) 141-. 
Military surveying circle. Delanges,P. Bologna 

Mm. I. It. 1 (pte. 2) (1806) 63-. 
Mirror for drawing in perspective. Schone- 

mann, P. Z. Nw. 10 (1874) 102-. 
Multiplication by a mechanical device. Ber- 

delle, C. As. Fr. C. E. (1887) (Pt. 2) 210-. 
Nautical instruments, and calculating appara- 
tus. Gelcich, E. Cztg. Opt. 5 (1884) 242-, 

253-, 268-, 277-; 6 (1885) 9 ; 7 (1886) 265-. 
Nicolas's gyrograph for tracing arcs of large 

circles. Gobin, A. Lyon A. S. Ag. 8 (1864) 

520-. 
Nurnberg, German Museum, mathematical 

collection. Giinther, S. Lpldina. 14 (1878) 

93-, 108-. 
, , instruments. Giinther, S. D. 

Nf. Vh. (1893) (Th. 2, Halfte 1) 32. 
Observations, mechanical calculation of results. 

Favaro, A. Yen. I. At. 2 (1876) 559-. 
Pantograph ; proof of chief theorem, etc. 

Haussner, A. Arch. Mth. Ps. 65 1880) 

334-. 
, scenographic, for projecting geometric 

figures. Magistrini, G. B. Bologna Opusc. 

Sc. 1 (1817) 289-. 
Pantographs. Ott, A. Cztg. Opt. 17 (1896) 

161-. 
, proof of properties (l r + 2 r + 3 r x r ) . Li- 

gowski, W. [1879] Arch. Mth. Ps. 65 (1880) 

329-. 
Parabola, apparatus for drawing. Thallmayer, 

V. Dingier 227 (1878) 430-. 
Parabolograph. Delone, N. B. Es. Ps.-C. S. 

J. 29 (Ps.) (1897) 76. 

Parallel lines, instrument for drawing. Nichol- 
son, W. Nicholson J. 2 (1799) 429-. 
, . Suverkrop, J. P. [1883] Sc. 

S. Arts T. 11 (1887) 73-. 

rule, new. B., R. Nicholson J. 9 (1804) 
212-. 

, . Boswell, J. W. Nicholson J. la 

(1806) 196- 
" Perspecteur-calquer," instrument for drawing 

in perspective. Breton, . Isere S. Bll. 27 

(1892) 659-. 
Perspective drawer. Brauer, E. Z. Mth. Ps. 

43 (1898) 163-. 

drawing instrument. Brunei-Bar ennes, 
de. Dingier 34 (1829) 325-. 

, Verly's instrument, report. Rodolphe, . 

Metz Mm. Ac. 20 (183^39) 258-. 

, scale for dividing vanishing lines. Cumber- 
land, G. Nicholson J. 16 (1807) 1-. 

Plagiograph aliter skew pantigraph. Sylvester, 
J. J. Nt. 12 (1875) 168. 

.history. Sylvester, J. J. Nt. 12 (1875) 214-. 

Plane surface, formation, law of progress of 
accuracy. Airy, (Sir) G. B. Ph. Mg. 42 
(1871) 107-. ' 



0080 Instruments 

Planigraph, projecting tortuous curve on plane. 

Delone, N. B. [1895] Vars. S. Nt. Tr. 

(1895-96) (C. R., Ps. C.) No. 2, 3 pp. 
Planimeter. Amsler, J. Ziir. Vjschr. 1 (1856) 

41-, 101-. 
, Amsler's. Decker, G. Dingier 140 (1856) 

27- ; 141 (1856) 29-. 

_, __. Weisbach, J. Giving. 4 (1858) 1-. 
, . Wittstein, T. Hann. Z. Archt. Vr. 7 

(1861) 289-. 
, . Petsch, . A. Pon. Chauss. 16 (1868) 

124-. 
, . Combes, C. P. M. A. Mines 19 (1871) 

278-. 
, . Bramwell, F. J. B. A. Rp. 42 (1872) 

401-. 

, . Purvis, F. P. Ph. Mg. 48 (1874) 11-. 
, . Rateau, A. As. Fr. C. E. (1896) (Pt. 

2) 130-. 
, , proof of principle. Steggall, . Edinb. 

Mth. S. P. 7 (1889) 25-. 
, , theory. Zhblkovskil,A. K. (xn) [1865] 

Kazan Un. Mm. (1864, Ps.-Mth. No. I), 

219-. 
, , . Aldis, W. S. N. Eng. I. Mn. E. 

T. 28 (1879) 211-. 
, , . Thire, A. A. Mines 11 (1887) 

121-. 
, Bouniakovsky's and modification. Decker, 

G. Dingier 140 (1856) 27-. 
, construction. Schulten, N. G. of. (vm) 

Helsingf. Ofv. 5 (1863) 245-. 
, Coradi's. ? Coradi, . V. Nost. Eng. Mg. 

32 (1885) 465-. 
, hatchet. Hill, F. W. [1894] L. Ps. S. P. 

13 (1895) 229-; Ph. Mg. 38 (1894) 265-. 
, history. Favaro, A. Forster Al. Bauztg. 

38 (1873) 68-, 93-. 
, . Wolf, R. Ziir. Vjschr. 37 (1892) 

111-; 38 (1893) 3-. 
- of Hohmann and Coradi. Fischer, G. Cztg. 

Opt. 5 (1884) 74-. 
, Lippincott. Greenhill, A. G. [1899] Sc. 

Abs. 3 (1900) 234. 
, Maass-, description. Gunther, F. Cztg. 

Opt. 7 (1886) 247-. 
, new. Eckert, , <& Hamann, . Cztg. 

Opt. 18 (1897) 125. 
, , description. Maevskij, J. A. [1889] 

Vars. S. Nt. Tr. (1889-90) (C. R., Ps. C.) 

No. 2, 7-. 
, form. Maxwell, J. C. Edinb. T. Sc. 

S. Arts 4 (1856) 420-. 
, (Beverley). Balfour, J. M. [1865] 

Edinb. Sc. S. Arts T. 7 (1868) 198-. 
, (1852). Baranoffsky, E. Helsingf. Acta 

4 (1856) 3-. 
, (1855). Bouniakoicsky, V. [1855] St 

Pet. Ac. Sc. fill. 14 (1856) 152-. 
polar. Amsler, J. Dingier 140 (1856) 321- ; 

141 (1856) 326-. 
, , Amsler's. Decker, G. Dingier 141 

(1856) 330-. 

, , . Sehinz, E. Bern Mt. (1857) 152-. 
, , . NehU, C. Giving. 20 (1874) 71-. 
, , , results. Hartogh Heys van Zou- 

teven, H. Arch. Neerl. 5 (1870) 440-. 



Instruments 0080 

Planimeter, polar, determination of constant. 

Schell, A. Wien SB. 56 (1867) (Ab. 2) 325-. 
, , general theory. Schell, A. Wien SB. 

58 (1868) (Ab. 2) 189- ; Carl Epm. 11 (1875) 

, ', note. Resal, H. C. B. 77 (1873) 

509-. 

, Eichard. ? Anon. Sc. Abs. 1 (1898) 635. 
, rolling, theory. Fenner, P. Cztg. Opt. 7 

(1886) 133-. 
, solutions of electric problems. Atkinson, 

L. B. Elect. 22 (1889) 702- ; 23 (1889) 

29-. 
, Trunk's. Hiibner, A. Arch. Mth. Ps. 44 

(1865) 337-. 

, Wetli's. Stampfer, S. Wien SB. (1850) 

(Ab. 1) 134-. 
Planimeters. Moberg, A . (vm) [1859] Helsingf. 

Ofv. 5 (1863) 53-. 

. Beck, A. Eiga Cor.-Bl. 40 (1898) 99-. 
, free. Bouniakowsky , V. St Pet. Ac. Sc. 

Bll. 2 (I860) 567-. 

and similar instruments. Kohlmorgen, 0. 
Westf. Vr. Jbr. (1890) 126-. 

of Wetli, Decher, and Amsler. Miller, 
W. H. Ph. Mg. 16 (1858) 230-. 

Problems of 3rd degree, instrument for solution. 

Simon, C. Les Mondes 4 (1864) 547-. 
Proportion -table, equivalent to sliding -rule 

13' 4" long. Everett, J. D. Ph. Mg. 32 

(1866) 350-. 

Protractor, semicircular, improved form. 
Stewart, J. N. Z. I. T. 3 (1870) 316-. 

for trisecting angles. Alexander, J. H. 
Silliman J. 7 (1849) 243-. 

Quadrature, instrument for. Boileau, P. C. E. 

15 (1842) 594-. 

Eefraction through prism; apparatus to illus- 
trate deviation of ray. Marcucci, S. Ev. 

Sc.-Ind. 27 (1895) 101-. 
Scale, accuracy of, and limit of perception. 

Neovius, E. Helsingf. Ofv. 23 (1881) 71-. 
" Scoliograph, unicursal," for drawing algebraic 

curves. Boguslawsky, A. [1881] Mosc. S. 

Nt. Bll. 57 (1882) (Pt. 2) 72-. 
Screw, use in mathematical instruments. 

Carl, P. Carl Epm. 2 (1867) 37-. 
Sectograph (for dividing lines and angles, &c.) . 

Jones, T. Tilloch Ph. Mg. 42 (1813) 401-. 
Sine and cosine quadrant. Schreiber, C. Gztg. 

Opt. 7 (1886) 38-. 
Spherical integrator, modification of a form of. 

Smith, F. J. Ph. Mg. 22 (1886) 147-. 

triangles, instrument for determining, by 
mechanical action. Penrose, F. C. As. S. 
M. Not. 36 (1876) 281-. 

Spherometer. Mayer, A. M. Am. J. Sc. 32 

(1886) 61-. 
, new. Kruss, H. Cztg. Opt. 12 (1891) 

63-. 
Spirals, Johnson's volutor for drawing. Booth, 

J. B. A. Ep. (1860) (Pt. 2) 60-. 
Square with parallel lines. Chaussenot, (I'Aine). 

Par. Bll. S. Encour. 43 (1844) 4-. 
Stanhope logical and arithmetical machine. 

Harley, (Rev.) R. N. S. W. E. S. J. 24 

(1890) 121-. 



37 



0080 Calculating Machines 

Stereoscopic drawing apparatus. Jensen, J. 

[1870] Arch. f. Ap. 4 (1871) 233-. 
Straight line apparatus, Hart's. Darboux, G. 

Bll. Sc. Mth. As. 3 (1879) 144-. 
Stupakoff's comparometer. Basford, G. M. 

Am. Eng. & Eailroad J. 73 (1899) 59, 169. 
Tachymeter, Cairo's. Puissant, L. C. E. 3 

(1836) 140, 200, 245-, 384. 
Tractonograph (instrument for describing 

curves of "tractory" nature). Kleritj, L. 

Dingier 305 (1897) 234-, 260- . 

of Kleritj, and rod-planimeter. Korselt, A. 
Z. Mth. Ps. 43 (1898) 312-. 

Trigonometer, instrument for solving spherical 

triangles. Braun, K. (xn) Mth. Term. Ets. 

1 (1883) 313- ; Mth. Nt. B. Ung. 1 (1882-83) 

283-. 
, Savy's. Le Grand, G. Aube Mm. S. Ag. 

5 (1854) 235-. 
Trisection of angle, instrument for. Burt, T. S. 

Beng. As. S. J. 1 (1832) 499-. 
, . Tate, T. Ph. Mg. 19 (1860) 

261- . 
, . Cassani, P. Yen. Aten. At. 

1 (1878) 163-. 
, . Longcliamps, G. de. As. Fr. 

C. B. (1893) (Pt. 2) 190-. 
.mechanical. Russell, A. H. Nt. 43 

(1891) 547-. 
angles, test. Ronisch, A. Cztg. Opt. 

16 (1895) 253-. 
Vernier for line or curve with unequal divisions. 

Artur, J. F. Par. Bll. S. Encour. 50 (1851) 

676-. 
, new form. Ludloic, H. H. V. Nost. Eng. 

Mg. 27 (1882) 196. 

or Nonius, priority. Breusing, A. [1879] 
As. Nr. 96 (1880) 129-. 

Verniers. Matzka, W. Grunert Arch. 34 
(1860) 334-. 

CALCULATING MACHINES. 

Addition machine. Goss, J. Tilloch Ph. Mg. 

41 (1813) 166-. 
Arithmetical machine, Cebysev's. Bool, V. G. 

von. Mosc. S. Sc. Bll. 91 (M. 1) (1894) 

12-. 
with continuous motion. Tchebitchef, 

P. L. Bv. Sc. 4 (1882) 402-. 

, supplementary explanation. Cebysev, 
P. L. Mosc. S. Sc. Bll. 91 (No. 1) (1894) 
22. 

machines, history. Mehmke, R. Prace Mt.- 
Fiz. 6 (1895) 177-. 

Arithmometer, Thomas's. Ettingshausen, A. 

von. Wien SB. 24 (1857) 16-. 
, . Reuleaux, F. Giving. 8 (1862) 

182- 

Hirn, G. A. Les Mondes 3 (1863) 



433- 
198- 



25-. 



Junge, A. Z. Mth. Ps. 9 (1864) 
Zillmer, . I. Act. J. 15 (*1870) 



, . Cavallero, A. Cuyper Bv. Un. 
(1880) 309-. 



Calculating Machines 0080 

Arithmometer, Thomas's, actuarial use. Gray, 

P. I. Act. J. 17 (*1873) 249-; 18 (*1875) 

20-, 123-. 
, , adaptation of assurance formulae to. 

Hannyngton, J. Assur. Mg. 12 (*1866) 

184. 
, , use. Hannyngton, (Maj.-Gen.). I. Act. 

J. 16 (*1872) 244-. 
, use. Him, G. A. A. G6n. Civ. 2 (1863) 

(pte. 2) 113-, 153-. 
, . Hancock, W. J. I. Act. J. 16 (*1872) 

265-. 
, in constructing tables. Garment, Z). 

I. Act. J. 22 (*1881) 368-; 23 (*1882) 

232. 
Calculating apparatus, arithmetical puzzles. 

Lucas, E. Bv. Sc. 45 (1890) 1-. 

based on Napier's rods. Bridge, J. Ph. 
Mg. 9 (1880) 191-. 

circle. Weiss, P. C. B. 131 (1900) 
1289-. 

instruments and machines. (2) Logarithmic 
scales. (3) Graphic processes. Ocagne,M.d\ 
A. Cons. Arts et Met. 5 (1893) 231-, 323-; 6 
(1894) 42-. 

machine. Babbage, C. Edinb. Ph. J. 8 
(1823) 122-. 

. Olivier, T. Par. Bll. S. Encour. 45 

(1846) 153-. 
. Nystrom, J. W. Franklin I. J. 21 

(1851) 262-. 
. Selling, E. D. Nf. Tbl. (1887) 234-; 

Wiirzb. Ps. Md. Sb. (1888) 148- ; Cztg. Opt. 

9 (1888) 3-. 

. Levdnen, S. Helsingf. Ofv. 38 
(1896) 26-. 

. Siedentopf, H. N.-Vorp. Mt. 30 (1899) 

xvii-. 
or arithmometer. Hoyan, . (vi Adds.) 

Par. Bll. S. Encour. 21 (1822) 355-. 
, . Thomas, . Moigno Cosmos 4 

(1854) 72-, 186-. 
. , Babbage's. Baily, F. Tilloch Ph. Mg. 

63 (1824) 355-. 
, . Menabrea, L. F. Taylor Sc. Mm. 

3 (1843) 666-. 

, . Brit. Ass. Comm. B. A. Bp. 
(1878) 92-. 

, . Menabrea, (le gen.) L. F. C. B. 99 
(1884) 179-. 

, , mechanical arrangements. Babbage, 

(Maj.-Gen.) H. P. B. A. Bp. (1888) 616-. 

for definite integrals. Moseley, H. B. A. 

Bp. (1841) (Pt. 2) 35-. 

, duplex. Kiittner, W. Dingier 300 
(1896) 199- . 

, <fec. Ramsing, H. M. Mth. Ts. 2 (1860) 

65-. 
, Fowler's. De Morgan, A. B. S. P. 4 

(1840) 243-. 
, Henri Genaille's. Genaille, H. As. Fr. 

C. B. (1894) (Pt. 2) 272-. 
, new. Lalanne, L. C. B. 9 (1839) 

319-. 

, . Fowler, . B. A. Bp. (1841) 
(Pt. 2) 39-. 

, . _Grant, G. B. Am. J. Sc. 8 (1874) 

277-. 



38 



0080 Calculating- Machines 

Calculating machine, new. Bailee, L. C. 

E. 109 (1889) 737-. 
, . Strehl, K. Cztg. Opt. 11 (1890) 

242-. 
, old. Cadell, W. A. Thomson A. Ph. 3 

(1814) 251-. 
for products, quotients, logs., and powers 

of numbers. Moseley, H. Ph. Mg. 30 (1847) 

, prospectus, &c. Slonimsky, C. Z. Crelle 

J. 28 (1844) 184-. 

for real roots of numerical equations. 
Moth, F. X. Wien D. 1 (1850) 105-. 

, report. Wiberg, . C. B. 56 (1863) 

330- . 
, Scheutz's. Meidinger, H. Dingier 156 

(1860) 241-, 321-. 

, Selling's. Poppe, A. Dingier 271 
(1889) 193-. 

machines. Helie, . Eure Eec. Tr. 2 

(1842) 170-. 

. Olivier, T. Par. Bll. S. Encour. 42 

(1843) 411-. 

. Jomard, E. F. Par. Bll. S. Encour. 

42 (1843) 548-. 

. Lauterburg, . Bern Mt. (1863) 20-. 

. Warren, T. P. B. Ph. Mg. 43 (1872) 

396-. 
. Edmondson, J. [1885] L. Ps. S. P. 7 

(1886) 81-; Ph. Mg. 20 (1885) 15-. 

. Davis, H. S. Pop. As. 4 (1897) 20-. 

. Torres, L. C. E. 130 (1900) 472-. 

, arithmograph. Gattey, . Par. Bll. 

S. Encour. 15 (1816) 50-. 
, continuous. Hele-Shaw, H. S. Phil. 

Trans. 176 (1886) 367-. 
, history. Mehmke, E. D. Mth. Vr. Jbr. 

3 (1894) 59-. 
and instruments. Ocagne, M. d'. Brux. 

S. Sc. A. 17 (1893) (Ft. 1) 84-. 

invented by Eussians. Bool, V. von. 
Mosc. S. Sc. Bll. 92 (No. 1) (1896) 33-. 

, theory. Stamm, E. Mil. I. Lomb. Ed. 

2 (1865) 360-. 
Calculation and calculating machines. Lucas, 

E. As. Fr. C. E. (1884) (Pt. 1) 111-. 
, mechanical aids. Sang, E. I. Act. J. 16 

(*1872) 253-. 
Calculations, instruments to aid. Thomson, G. 

[1896] Sc. S. Arts T. 14 (1898) 172-. 
Chinese- Japanese calculating machine, and 

Chinese Swan-Pan (calculating table) . West- 

phal, A. (XH) D. Gs. Ostas. Mt. 1 (1873- 

76) (Heft 8) 27-, (Heft 9) 43-. 
Efficiency, apparatus for calculating. Boys, 

C. V. (ix) [1882] L. Ps. S. P. 5 (1884) 28-; 

Ph. Mg. 13 (1882) 193-. 
Logarithmic calculating rules, Lambert's. 

Schweigger, J. S. C. Schweigger J. 14 (1815) 

115-. 
Slide-rule. Burg, A. Wien Jb. Pol. I. 16 

(1830) 101- . 

. Burdon, . C. E. 58 (1864) 573-. 

. Mackesy, W. H. Medley I. Eng. 4 

(1867) 349-. 
. Schwind, F. von [1873] Innsb. Nt. 

Md. B. 4 (1874) liv-. 



Models 0080 

Slide-rule. Boys, C. V. Nt. 32 (1885) 627-. 
, employment. Herrmann, E. Oestr. Z. 

Brgw. 15 (1867) 193-. 
, . Charnoz, J. Ev. Mar. et Col. 57 

(1878) 493-. 

, English. Sedlaczek, E. Hammer- 
schmidt Al. Oestr. Z. (1846) 439-, 451-, 
465-, 478-; (1847) 182-, 221-, 318-, 342-, 
365-, 390-, 401-. 

, Fuller's. Fenton, J. J. Viet. E. S. T. 

22 (1886) 57-. 
for gauging casks. Young, (Dr) T. QJ. 

Sc. 16 (1823) 357-. 

, gunner's. Smith, John T. Madras 
Eng. Ep. 2 (1846) 14-. 

, model. Beghin, A. As. Fr. C. E. 
(1900) (Pt. 1) 127-. 

, new. Gallice, G. C. E. 128 (1899) 163-. 

, . Puller, . Hann. Archt.-Vr. Z. 
46 (1900) 203-. 

, __ calculating. Fuller, G. (xn) [1879] 

Belfast NH. S. P. (1878-80) 36-. 
, form of . Beghin, A. As. Fr. C. E. 

(1899) (Pt. 2) 142-. 

, proposed addition. Schweth, W. D. 
Nf. Vh. (1900) (Th. 2, Hdlfte 1) 66-. 

, proposed forms. Darwin, G. H. L. 
Mth. S. P. 6 (1875) 113. 

, radial cursor. Lanchester, F. W. [1895] 

L. Ps. S. P. 14 (1896) 8-; Ph. Mg. 41 (1896) 

52-. 
, solution of equations in three variables. 

San Roberto, P. di. [1867] Tor. Mm. Ac. 25 

(1871) 53-. 

, treatment of equation in two variables. 
San Roberto, P. di. Tor. At. Ac. Sc. 2 
(1866-67) 454-. 

, use. Boys, C. V. V. Nost. Eng. Mg. 

33 (1885) 512- . 

rules, Everett's proportion-table. Everett, 
J. D. Ph. Mg. 32 (1866) 350-. 

, Fuller's calculating helix, and historical 

notes on calculating instruments with log- 
arithmic divisions. Favaro,A. Ven. I. At. 
5 (1879) 495-. 

1 logarithmic. Sedlaczek, E. Hammer- 

schmidt Al. Oestr. Z. (1847) 493-, 507-, 
521-, 531-. 

, modified. Mannheim, A. N. A. Mth. 

12 (1853) 327-. 

MODELS. 

Cubic surface with 27 real lines. Wiener, . 

D. Nf. Tbl. (* 1868) 56-. 
. Blythe, W. H. Camb. Ph. 

S. P. 8 (1895) 241-. 
. Taylor, H. M. Camb. Ph. 

S. T. 18 (1900) 375-. 
, Wiener's model. Cayley, A. 

[1871] Camb. Ph. S. T. 12 (1879) 366-. 

surfaces, construction of models. Blythe, 
W. H. QJ. Mth. 29 (1898) 206-. 

, model by Eodenburg. Korteweg, D. J. 
N. Arch. Wisk. 20 (1893) 63-; Fschr. Mth. 
(1893-94) 83. 

Cylindroid. Ball, R. S. Ph. Mg. 42 (1871) 
181- ; Am. As. P. (1884) 52-. 



0090 



Aids to Calculation, Graphical Processes 



0090 



Descriptive geometry, models. Didier, , & 

Evrard, . Par. S. Phlm. Bll. (1833) 177-. 
Ellipsoid, model of the centre-surface. Hummer, 

E. E. Berl. Mb. (1862) 426-. 
Goniometrical instruction. Hoza, F. Arch. 

Mth. Ps. 61 (1877) 108-. 
Kinematic models, epicycloids, linkwork. 

Schilling, F. D. Nf. Vh. (1898) (Th. 2, 

Halfte 1) 6-. 
Mathematical models, use. Emch, A. Kan. 

Ac. Sc. T. 14 (1896) 90-. 
Minimal surface, model in plaster. Schwarz, 

H. A. Berl. Mb. (1872) 122-. 
Paraboloids, hyperbolic, model. Olivier, T. 

Par. S. Phlm. N. Bll. (1832) 184-. 
Pencils, thin, models. Kummer, E. E. Berl. 

Mb. (1860) 469-. 
Bonayne's cubes. Hennessy, H. Ph. Mg. 39 

(1895) 183-. 
Buled surface, 3rd order. La Gournerie, J. de. 

Par. A. Cons. 6 (1866) 205-. 
Sections of quadric surfaces. Wiener, . 

Karlsruhe Nt. Vr. Vh. 10 (1888) (Sb.) 50-. 
Stereographic equatorial projection of a sphere, 

transformation by means of a form of the 

Peaucellier cell. Phillips, A.W. B. A. Ep. 

(1884) 649. 
Subdivision of an arbitrary angle by models. 

Strauss, A. Arch. Mth. Ps. 12 (1894) 177-. 
Thread models of developable surfaces. 

Schaute, P. H. Amst. Ak. Vs. [2] (1894) 

8-. 

0090 Aids to Calculation, Graphical 
Processes. 

Abaci adapted to equations with three and four 

variables. Ocagne, M. d\ Brux. S. Sc. A. 

22 (1898) (Pt. 1) 78-. 
, graphical calculation by hexagonal. 

Lallemand, C. C. E. 102 (1886) 816-. 
Abacus. Knott, C. G. Jap. As. S. T. 14 

(1886) 18-. 
. Duporcq, E. C. E. 127 (1898) 265-. 

for diurnal and semi-diurnal tides. Ocagne, 
M. d'. C. E. 122 (1896) 298-. 

, new kind. Goedseels, . Brux. S. Sc. 
A. 22 (1898) (Pt. 1) 43-. 

with 16 and 18 variables. Lafay, A. C. E. 
119 (1894) 1195-. 

Algebraic functions, representation. Ott, C. de. 

Par. A. Cons. 6 (1866) 450-. 
Anamorphosis, problem. Lecornu, L. C. E. 

102 (1886) 813- . 
Arbitrary functions, development. Perry, J., 

d- Hunt, H. F. [1895] L. Ps. S. P. 14 (1896) 

1-; Ph. Mg. 40 (1895) 506- . 
Arc, construction when centre is inaccessible. 

Prevost, P. Bb. Un. 49 (1832) 98-. 
Archimedes' screw, applications in graphical 

calculation. Sayno, A. Mil. I. Lomb. Ed. 

7 (1874) 163-. 
Arithmetic mean, determination. Ivancich, 

J. N. Wien Berg-Hm. Jb. 24 (1876) 295-. 
Calculation, methods of simplification. Goed- 
seels, E. Brux. S. Sc. A. 23 (1899) (Pt. 2) 1-. 
Chess-board, use, for arithmetical problems. 



Delanncy, . As. Fr. C. E. (1886) (Pt. 2) 

183-. 
Circle divider, description. Laussedat, (le col.) 

. As. Fr. C. E. (1885) (Pt. 1) 97-. 
, division, &c., graphic solution. Pe'reaux, E. 

A. Gen. Civ. 17 (1870-71) 735-. 
Circular arcs, graphic rectification, and con- 
struction of cyclic curves. Schlomilch, 0. 

Schlomilch Z. 2 (1857) 330-. 
Coefficients of algebraic equations, representa- 
tion. Nehls, C. [1893] Hamb. Mth. Gs. Mt. 

3 (1900) 139-. 
Colours in nature, law of multiple proportions. 

Collins, F. H. Nt. 52 (1895) 438. 
, . Lovibond, J. W. Nt. 

52 (1895) 547, 577. 
, . Cattell, J. McK. Nt. 

52 (1895) 547. 
Complex numbers, representation. Broch, 0. J. 

As. Fr. C. E. 3 (1874) 1174-. 
"Compteurs logarithmiques." Cauchy, A. L. 

C. E. 40 (1855) 1009- ; 44 (1857) 257-. 
Construction of surfaces by plane sections. 

Cardinaal, J. Amst. Ak. Vs. M. 



198- ; Fschr. Mth. (1889) 665-. 
Cube, duplication by geometry. Fontes, . 

Toul. Ac. Sc. Bll. 1 (1898) 129-. 
, , graphic approximation. Gergonne, 

J. D. Gergonne A. Mth. 10 (1819-20) 242-. 
, , by means of parabola. Longchamps, 

G. de. Mathesis 16 (1896) 245-. 
, , mechanical construction of curves for. 

Matthiessen,L. Arch. Mth. Ps. 48 (1868) 229-. 
roots, geometrical construction. Montucci, 

H. C. E. 44 (1857) 773-. 
Curve systems and their application to differ- 
ential equations. Ldska, W. Prag Sb. 

(1890) 1 (Mth.-Nt.) 222-. 
Curves, graphical treatment of experimental. 

Lehfeldt, R. A. [1900] L. Ps. S. P. 17 

(1901) 605- . 
Deduction of differential equations from graphs. 

Warder, E. B. Science 4 (1896) 345. 
Development of arc of circumference of given 

radius, tables for calculations. Prat, , 

<& Bancarel, . (vm) A. Cond. Pon. 

Chauss. 6 (1862) 49-. 
Diagrammatic and mechanical representation 

of propositions and reasonings. Venn, J. 

Ph. Mg. 10 (1880) 1-. 
. McColl, H. Ph. 

Mg. 10 (1880) 168- . 
Diagrams for ascertaining percentage relation. 

Smith, W. B. A. Ep. (1890) 982-. 
, employment for representation of logical 

propositions. Venn, J. [1880] Camb. Ph. S. 

P. 4 (1883) 47-. 
Drawing of curves by their curvatures. Boys, 

C. V. [1893] L. Ps. S. P. 12 (1894) 345- ; 

Ph. Mg. 36 (1893) 75-. 

Economic problems, monopolies, graphic repre- 
sentation by series of hyperbolas. Marshall, 

A. (vra) [1873] Camb. Ph. S. P. 2 (1876) 

318-. 
Ellipse, graphic rectification. Somoff,J. [1850] 

St Pet. Ac. Sc. Bll. 9 (1851) 97-. 
, spacing the. Grant, G. B. Franklin I. J. 

127 (1889) 280-. 



40 



0090 



Aids to Calculation, Graphical Processes 



0090 



Ellipses, method of describing. Williams- 
Ellis, J. C. [1870] Camb. Ph. S. P. 2 
(1876) 197-. 

Empirical formulae, calculation. Hopkinson, 
J. Mess. Mth. 2 (1873) 65-. 

Equation y = ax n , determination of n. Durand, 
W. F. Franklin I. J. 143 (1897) 188-. 

Fourier series, graphic development in. Perry, 
J. Elect. 35 (1895) 285-. 

Functions connected by linear equation and 
graphic solution. Delafon, R. Bv. Mar. et 
Col. 79 (1883) 305-. 

of several variables, graphical evaluation. 
Adler, A. Wien Ak. Sb. 94 (1887) (Ab. 2) 404-. 

Graphic arithmetic, applications to theory of 
numbers. Arnoux, G., & Laisant, C. A. 
As. Fr. C. B. (1900) (Ft. 2) 36-. 

calculation, 1st operations. Favaro, A. 
Yen. At. 1 (1871-73) 1391-. 

calculus, note on question. Florov, P. S. 
(xn) Kharkov Mth. S. Com. (1880) 36-. 

integration. Solin, J. M. Prag Ab. 5 
(1872) 10 pp. 

. Pickering, E. C. Am. Ac. P. 10 

(1875) 79-. 
. Solin, J. M. Prag Sb. (1879) 195-. 

, and application to statics of external 
forces on a beam. Baldermann, 0. Forster 
Al. Bauztg. 46 (1881) 24-, 33-, 49-, 97. 

, applications. Nassau, J, Bv. Un. 
Mines 16 (1884) 243-, 579- ; 17 (1885) 1- ; 
20 (1886) 1-, 475-; 21 (1887) 85-, 308-, 
572-; 22 (1887) 1-. 

of certain types of differential equations. 

Petrovitch, M. Par. S. Mth. Bll. 27 (1899) 200-. 
(liquid apparatus). 

Petrovitch, M. Am. J. Mth. 22 (1900) 1-. 
curves. Krdhnass, A. Chili S. Sc. 

Act. 4 (1894) 3-. 
differential equations. Petrovitch, M. 

C. E. 124 (1897) 1081-. 
partial differential equations. Coulon, 

J. C. E. 130 (1900) 1378-. 

interpolation. Dittmar, W. Ph. Mg. 21 
(1861) 139-. 

and integration. Darwin, G. H. B. A. 

Ep. (1876) (Sect.) 13; Mess. Mth. 6 (1877) 
134. 

method, applications. Pickering, E. C. 
(vra) Am. Ac. P. 9 (1874) 222-. 

methods in geometry. Carballo, J. M. R. 
(xn) [1881] Barcel. Ac. Mm. 1 (1878) 223-. 

mechanical science. Hele-Shaw, H. 

S. B. A. Bp. (1892) 373-; (1893) 573-. 
research. Gilbert, G. K. Smiths. 

Misc. Col. 33 (1888) Art. 4, 4 (bis)-; (Wash. 

Ph. S. Bll. 10 (1888).) 
of solving practical problems. Reynolds, 

0. [1875] Manch. Lt. Ph. S. P. 15 (1876) 55-. 

phoronomy. Kapp, G. Z. Mth. Ps. 17 
(1872) 419-. 

problem. Tramontini, G. [1806] Mod. S. 
It. Mm. 13 (1807) 38-. 

tables and anamorphic geometry, priority 
claim. Lalanne, L. L. C. C. B. 85 (1877) 
1012-. 

technology, apparatus for separation of 



polynomial into factors. Arnoux, G. Par. 

S. Mth. Bll. 21 (1893) 87-. 
Graphic transformer. Trotter, A. P. Elect. 

33 (1894) 463-. 
Graphics. Vose, G. L. V. Nost. Eng. Mg. 12 

(1875) 529-. 
Gunter's scale, new arrangement of. Nicholson, 

W. Nicholson J. 1 (1797) 372-. 
Harmonic curves, graphical analysis. Wedmore, 

E. B. Elect. 35 (1895) 512-. 
Imaginary functions, graphic representation. 

Siebeck, H. Crelle J. 55 (1858) 221-. 
Integral curve applied to division of volumes. 

Brauer, E. Z. Mth. Ps. 42 (1897) 272-. 

of r n de found graphically. Price, W. A. 
Elect. 36 (1896) 73-. 

Integrals of curves and moments of inertia. 

Nehls, C. Z. Bauw. 39 (1889) 293-. 
Interpolation-curves, a correction sometimes 

required. Rayleigh, (Lord). Ph. Mg. 42 

(1871) 441-. 
Isomers, theory (ramifications). Cayley, A. 

Ph. Mg. 47 (1874) 444-. 
Japanese arithmetic, use of geometry. Berson, 

. Toul. Ac. Sc. Mm. 3 (1891) 268-. 
Lagrange-Newton analytical parallelogram. 

Sincov, D. Kazan S. Ps.-Mth. Bll. 9 (1900) 

44-; Fschr. Mth. (1899) 49-. 
Line construction for solution of system of 

linear equations, regarded as a configuration. 

Berg, F. J. van den. Amst. Ak. Vs. M. 5 

(1889) 267- ; Fschr. Mth. (1888) 76. 
Logarithmic charts, scale lines. Boys, C. V. 

Nt. 52 (1895) 272-. 

computations. Howe, H. A. [1883] Sid. 
Mess. 2 (* 1883-84) 45-. 

coordinates. Vincent, J. H. B. A. Bp. 
(1898) 159-. 

paper for engineers. Saussure, R. de. Bv. 
Sc. 2 (1894) 743-. 

Logarithms, mechanical calculation. Pockling- 

ton, H. C. Nt. 61 (1899-1900) 469. 
Logical diagrams for n terms. Mdrquand, A. 

Ph. Mg. 12 (1881) 266-. 
Mechanical geometrical proof. Lang, V. van. 

Exner Epm. 21 (1885) 355-. 
Medium value of set of normal variants, geo- 
metric determination. Galton, F. [1899] 

Nt. 61 (1899-1900) 102-. 
Moments of inertia of solids of revolution. 

Lopes Banhos, G. C. G. Teix. J. Sc. 5 

(*1883) 125- ; Fschr. Mth. (1884) 792. 
Mortality equations and curves. Isely, L. 

Neuch. S. Sc. Bll. 17 (1889) 38-. 
Multiplication, method of performing. Berdelle, 

C. As. Fr. C. E. (1884) (Pt. 2) 584-. 
Nomography, graphic calculation. Ocagne, 

M. d'. Ens. Mth. 2 (1900) 207-. 
Order of magnitudes, graphical representation. 

Erdmann, H. Z. Nw. 66 (1893) 73-. 
Perspective drawing, method. Williams- Ellis, 

J. C. [1870] Camb. Ph. S. P. 2 (1876) 197-. 
Physical laws deduced from empirical curves. 

Schiaparelli, G. V. Mil. Effem. (1867) 3-. 
. Pucci, E. N. Cim. 27 

(1890) 220- ; 28 (1890) 111-. 
Planimeters and similar instruments. Kohl- 

morgen, O. Westf. Vr. Jbr. (1890) 126-. 



0400 Arithmetic 

Practical conformal representation by current 

sheets. Kelvin (Lord). Elect. 29 (1892) 

553, 634. 
Probable values of constants in u=a + by. 

Anon, 's Gravenh. I. Ing. Ts. (1884-95) 

(Verg.) 68-. 
Problems, solution by cycloid. Guimaraes, E. 

G. Teix. J. Sc. 6 (1885) 85-; Fschr. Mth. 

(1884) 492. 
of third and fourth degrees, solution. 

Lame, G. J. Gen. Civ. 1 (1828) 435-. 
Quadrature, graphical method. Collignon, E. 

Par. S. Mth. Bll. 15 (1887) 145-. 
Eepresentation of physical properties of sub- 
stances by surfaces. Peddie, W. Edinb.Mth. 

S. P. 2 (1884) 33-. 
z=f(x, y). Lalanm, L. Par. S. Phlm. 

P.-V. (1843) 71-. 
Saturated carbides (C n H' 2n + 2 ), representation. 

Brunei, . Bordeaux S. Sc. Mm. 5 (1895) 

xxxix-. 
Series of experiments, graphic representation. 

Sebelien,J. (xn) Ts. Mth. 1 (1883) 186- ; 

Fschr. Mth. 16 (1887) 182-. 
Solutions by construction. Hill, T. Am. As. 

P. (1855) 62-. 
Spherical triangles, graphic method of solution. 

Smith, C. H. Am. J. Mth. 6 (1884) 175-. 
" Spiraligrafico meccanico," instrument for 

graphical calculations. Sayno, A. Mil. I. 

Lomb. Ed. 7 (1874) 499-. 
Statistical science, new step. Galton, F. Nt. 

51 (1894-95) 319. 
Statistics, graphical presentation. Haupt, 

L. M. Franklin I. J. 148 (1899) 384-. 
, mathematical representation. Edgeworth, 

F. Y. B. A. Ep. (1898) 791. 
Terms of imprisonment, statistics and curves. 

Galton, F. Nt. 52 (1895) 174-. 
Theory of contours and its applications in 

physical science. Peddie, W. Edinb. Mth. 

S. P. 4 (1886) 25-, 61-. 
Transcendent numbers, graphic construction. 

Laisant, C. A. Par. S. Phlm. Mm. Cent. 

(1888) 63-. 
Triangle for calculation purposes. Chenevier, 

. As. Fr. C. E. (1886) (Pt. 1) 85. 
, graphical solution. Weisz, J. A. (xn) 

Mag. Ak. Ets. (1858) 73-. 
Vector diagrams, use, for representation of 

diurnal variation of earth's magnetism. 

Chree, C. Nt. 61 (1899-1900) 490. 
N.B. For references to other papers belonging 
to 0000-0090 see Special Sections. 

ARITHMETIC AND ALGEBRA. 

Foundations of Arithmetic. 
0400 General. 

Additive theory of numbers. Vahlen, K. T. 

Crelle J. Mth. 112 (1893) 1-. 
Arithmetic, foundation of modern. Montessus, 

E. de. Ens. Mth. 1 (1899) 185-. 
, principles. Volkov, M. S. Kazan S Nt 

(Ps.-Mth.) P. 4 (1886) 5-. 
, theories. Frege, . Jena. Sb. (1885) 94-. 



Arithmetic 0400 

Arithmetic, two problems. Schlegel, M. Arch. 

Mth. Ps. 11 (1892) 93-. 
Arithmetical puzzle. Gopel, A. GrunertArch. 

6 (1845) 34-. 
Arithmology. Terquem, 0. N. A. Mth. 9 

(1850) 174-. 
, elementary. Lalanne, L. C. E. 11 (1840) 

903-. 
, application to algebra. Lebesgue, V. A. 

N. A. Mth. 1 (1862) 219-, 254-, 405-. 
Axiom of Archimedes. Stolz, 0. Mth. A. 39 

(1891) 107-. 
Axioms of arithmetic. Milhaud, G. Ev. Sc. 

40 (1887) 46-. 
Cipher, value. Vencat-Juggarow , G. Madras 

J. 2 (1835) 369-. 
Code, arithmetical. Claudel, . (viz) A. 

Cond. Pon. Chauss. 4 (1860) 92-. 
Decimals. Peacock, A. B. A. Ep. (1842) 

(pt. 2) 10-. 

. Spitzer, S. Grunert Arch. 9 (1847) 117-. 
"Dual arithmetic," new, applied to military 

calculations. Byrne, O. (ix) [1866] Un. 

Serv. I. J. 10 (1867) 37-. 
Equivalence, arithmetic conception. Min- 

kowski, H. Crelle J. Mth. 100 (1887) 449-. 
Euclid's books VII, VIII, IX, summary. 

Peano, G. Ev. Mt. 1 (1891) 10-. 
Fractions, certain. Tucker, E. L. Mth. S. 

P. 10 (1878-79) 123, 225-. 
, vulgar. A., S. (vr Adds.) Tilloch Ph. 

Mg. 48 (1816) 204. 
, , a set. Stouvenel, V. Liouv. J. Mth. 5 

(1840) 265-. 
Geometry, application to arithmetic. Ricour, 

A. Douai Mm. S. Ag. 11 (1873) 279-. 
Infinite quantities. Oltramare, G. Gen. I. 

Nt. Mm. 4 (1856) 1-. 

real integers, and their relation to each 
other. Cantor, . D. Nf. B. (*1883) 57. 

Lagrange's "Solution d'un probleme d'arith- 
m^tique," remarks on preface. Plana, G. 
Tor. Mm. Ac. 20 (1863) 87-, 109-. 

Magnitude : fundamental notions. Calinon, A . 
Nancy S. Sc. Bll. (1897) 39-. 

and its measure. Zaremba, S. Wiad. Mt. 
1 (1897) 58-. 

New mathematics, interpretation of old by. 
Halsted, G. B. Texas Ac. Sc. T. 1 (No. 2) 



Number and allied conceptions, definition. 

Thiele, T. N. Kjrfb. Dn. Vd. Selsk. Skr. 2 

(* 1881-86) 451- ; Fschr. Mth. (1887) 64-. 
, conception. Kronecker, L. Crelle J. Mth. 

101 (1887) 337-. 
_, _. Keferstein, H. Hamb. Mth. Gs. Mt. 

2 (1890) (Festschr. Tl. 2) 119-. 
, . Peano, G. Ev. Mt. 1 (1891) 87-, 256-. 
, . Hilbert, D. [1899] D. Mth. Vr. Jbr. 

8 (1900) (Heft 1) 180-. 
, definition. Laurent, H. N. A. Mth. 17 

(1898) 277-. 
Numeral and metral systems. Garbett, E. L. 

Glasg. Ph. S. P. 8 (1873) 329-. 
Numeration. Gergonne, J. D. Gergonne A. 

Mth. 21 (1830-31) 329-. 
. Eocquigny, F. [G.] de. Les Mondes 1 

(1881) 266-. 



42 



0410 



Rational Numbers; Arithmetical Operations 



0410 



systems. Cantor, G. Z. Mth. 

121-. 
son. Stein, J. P. Crelle J. 1 



Numeration, 

Ps. 14 
- , comj 

(1826) 369-. 
Numerical system, new. Eissfeldt, F. Des 

Moines Anal. 2 (1875) 151-. 
Proportionality, conception. Bustelli, A. M. 

G. Mt. 13 (1875) 82-. 
Step fractions. Gohierre de Longchamps, . 

G. Mt. 15 (1877) 299-. 
Variations of quantity, intensity. Bordoni, A. 

(vi Adds.) Opusc. Mt. Fis. 1 (1832) 97-. 



0410 Rational numbers; arith- 
metical operations. 

Approximate arithmetic. Heppel, G. Educ. 
Times 40 (1887) 417-. 

methods. Lodge, A. Mth. Gz. No, I 
(1894) 4-, No. 3 (1894) 21-. 

Approximate multiplication and division. 
Robertson, J. A. I. Act. J. 32 (1896) 160-. 

numbers, errors in products and powers. 
Anon, (vi 540) Gergonne A. Mth. 11 
(1820-21) 376-. 

Approximation. Anon, (xi 51) N. A. Mth. 5 

(1866) 407-. 
, Fontaine's method. Coellio da Maia, M. J. 

Lisb. Mm. Ac. Sc. 1 (1797) 503-. 
Approximations in arithmetic. Kopp, G. 

Neuch. Bll. (1846-47) 352-. 
, numerical. Guilmin, A. N. A. Mth. 1 

(1842) 249-, 487-. 
, . Lionnet, E. N. A. Mth. 8 (1849) 

266-; 12 (1853) 177-. 

, , relative to the four fundamental opera- 
tions. Bredin, C. (xn) [1858] Doubs S. 

Mm. 5 (1861) 361-. 

of roots, powers, &c. Bourdat, . Grenoble 
Ac. Delph. Bll. 3 (1850) 447-. 

Arithmetic, first stage. Quick, (Eev.) R. H. 

Educ. Times 41 (1888) 227-. 
, fourth process. Schulze, E. Arch. Mth. 

Ps. 3 (1886) 302- ; 9 (1890) 320-. 
, solutions without proportion. Berard, & 

Gergonne, . Gergonne A. Mth. 8 (1817- 

18) 353-. 
Arithmetical operations, &c. Houzeau, J. C. 

Brux. Ac. Bll. 40 (1875) 74-; 41 (1876) 

961-. 
, fundamental generalization. Schapira, 

H. D. Nf. Tbl. (*1882) 128-. 

, , order of precedence. Capelli, A. 
Nap. Ed. 39 (1900) 138-. 

, inverse. Mainardi, G. [1849] Mod. S. 

It. Mm. 25 (1852) 1-. 

, number of digits in results. Vinot, J. 
A. Gen. Civ. 2 (1863) (pte. 2) 172-. 

, particular cases of more general. Faure, 

H. Par. S. Phlm. P.-V. (1847) 31-. 
, signs. Le Paige, C. Brux. S. Sc. A. 

16 (1892) (Pt. 2) 70-. 
summations. Ocagne, M. d'. G. Teix. J. 

Sc. 7 (1886) 117-. 
Binary arithmetic. Farquhar, H. Science 2 

(*1883) 755-. 



Calculation, Doms' method. Mewes, R. Dingier 

315 (1900) 547-. 
, means of avoiding errors. Cauchy, A. L. 

C. B. 11 (1840) 789-, 826. 
, numerical, notes. Houzeau, J. C. Brux. 

Ac. Bll. 20 (1865) 614- . 
Calculations, arithmetical, involving large 

numbers. PervuSin, I. Kazan S. Ps.-Mth. 

Bll. 4 (1895) (Prot.) 74-. 
, checking, note. Walenn, W. H. [1879] 

Ph. Mg. 9 (1880) 56-. 
, instruments to aid. Thomson, G. [1896] 

Sc. S. Arts T. 14 (1898) 172-. 
Computation for scientific purposes. Lupton, S. 

Nt. 37 (1888) 237-, 262-. 
. Ramsay, W., & Young, S. Nt. 

37 (1888) 294-. 
. Scott, E. E. Nt. 37 (1888) 

319. 
. King, G. Nt. 37 (1888) 319-. 

of sums of products. Orlov, A. P. Kazan 
S. Nt. (Ps.-Mth.) P. 4 (1886) 59. 

. Preobraienskij, V. V. Kazan 

S. Nt. (Ps.-Mth.) P. 4 (1886) 72-. 
Continued product of numbers without use of 

logs., by formula and table. Sylvester, J. J. 

Ph. Mg. 7 (1854) 430-. 
Cube and cube-root, obtaining by Homer's 

method. Rusch, M. Arch. Mth. Ps. 67 

(1882) 291-. 

root. Nievengloski, G. H. N. A. Mth. 10 
(1851) 86-. 

extraction. Midy, . N. A. Mth. 3 
(1844) 234-. 

. GySry, S. (xn) Mag. Ak. Ets. 

(1851)282-; (1852) 62-. 
. Hofmann, F. Grunert Arch. 22 

(1854) 240. 
. Forestier, C. N. A. Mth. 17 

(1858) 7-. 
. Gouzy, E. A. Arch. Mth. Ps. 49 

(1869) 101-. 
, abridged. Hill, C. J. D. Crelle J. 

11 (1834) 262-. 
. , . Miiller, J. H. T. Grunert Arch. 

8 (1846) 46-. 
, . Genocchi, A. N. A. Mth. 17 

(1858) 136-. 
, . Dostor, G. Arch. Mth. Ps. 64 

(1879) 321-. 
, . Bernardi, G. G. Mt. 35 (1897) 

112-, 353. 

, integers. Delorme, . [1838] 
Amiens Mm. (1839) 251-. 

, new method. Nicholson, P. Tilloch 

Ph. Mg. 56 (1820) 360-. 

roots by inspection. Evans, J. Tilloch Ph. 
Mg. 51 (1818) 443-. 

Decimal notation, ancient and modern. 
Piccard, . Laus. Bll. S. Vd. 6 (1859) 
163- . 

numbers, multiplication. Vervaet, J. 
Casopis 15 (1886) 24-; Fschr. Mth. (1886) 
127. 

operations, simplifying and checking. 
Cauchy, A. L. C. E. 11 (1840) 847-. 

places, error from neglected. Hoppe, R. 
[1845] Crelle J. 40 (1850) 141-. 



43 



0410 



Rational Numbers; Arithmetical Operations 



Decimal point, determination of position in 

multiplication and division. Jelinek, V. 

Casopis 20 (1891) 35- ; Fschr. Mth. (1891) 

166. 
Decimals; approximation. Amiot, B. Rouen 

Ac. Tr. (1841) 161- ; N. A. Mth. 10 (1851) 

238-. 
, multiplication. Bernauggi, I. Verona Mm. 

S. It. 6 (1792) 1-. 
, recurring, division by 11. Transon, A. 

N. A. Mth. 4 (1845) 227-. 
, , formula for conversion. Trembloy, . 

N. A. Mth. 1 (1842) 522-. 
, reduction to fractions. Ponte-Horta, F. da. 

Lisb. J. Sc. Mth. 1 (1868) 275-. 
Discontinuous geometry. Bugaev, N. V. [1890] 

Bee. Mth. (Moscou) 15 (1891) 600- ; Fschr. 

Mth. (1891) 726. 
Division, abridged. Finck, B. N. A. Mth. 4 

(1845) 328-, 658-; 5 (1846) 599-. 
, . Crelle, A. L. Crelle J. 31 (1846) 167-. 
, . Crosson,A. N. A. Mth. 5 (1846) 244-. 
, . Guy, . N. A. Mth. 5 (1846) 460-. 
, . Verhulst, P. F. N. A. Mth. 5 (1846) 

629-. 
, . Spitzer, S. [1850] Haidinger B. 7 

(1851) 175-. 



0410 

Hummel, F. H. 



, . Lionnet,E. N. A. Mth. 11 



, . Hausel,. 
, . Rouche,E. 
, . Henry, C. 
, long. 



N. A. Mth. 14 
N. A. Mth. 16 
N. A. Mth. 20 



1852 
1855 
1857 
1881 



148-. 
129-. 
152-. 
213-. 



Dodgson, G. L. Nt. 57 (1897-98) 
Nt. 57 (1897- 
N. A. 



, . Christie, R. W. D. 

98) 390-. 
, and ordinary. Turquan, . 

Mth. 13 (1854) 170-. 

, singular case. Adville, . N. A. 
Mth. 11 (1852) 100-. 

of approximate numbers, rule. Verhulst, 
P. F. Brux. Ac. Bll. 13 (1846) 696-. 

, arithmetical, new rule. Peirce, C. 8. 

Science 2 (*1883) 788-. 
, , theory. Faucheux, L. E. N. A. Mth. 

14 (1854) 51-. 
, complementary. Ter quern, O. N. A. Mth. 

6 (1847) 425-. 
, . Meech, L. W. Des Moines Anal. 9 

(1882) 97-. 

and evolution, rationale of processes. 
Niederrist, . Grunert Arch. 35 (1860) 
201-. 

, Fourier's, ^and application to square root. 
Schaar, M. Brux. Ac. Bll. 18 (1851) (pte. 2) 

, Gerbert's rules. Friedlein, G. Z. Mth. 

Ps. 9 (1864) 145-. 
, new method. Kostenec, A. Casopis 15 

(1886) 74-; Fschr. Mth. (1886) 127-. 
, numerical, easy method. Crelle, A. L. 

Crelle J. 13 (1835) 209-. 
, results in. Langley, E. M. Mth. Gz. 1 

(1900) 205-, 275-. 

and subtraction, extended. Callegari, P. 
Bologna N. Cm. 6 (1844) 513- ; 7 (1844) 529-. 

Divisors, fractional, in arithmetic. Terquem, O. 
N. A. Mth. 8 (1849) 246-. 



Evolution by subtraction. 

Ph. Mg. 10 (1880) 190-. 
Factorisation and factorial calculation. Paci- 

notti, L. Pisa A. Un. Tosc. Sc. Cosm. 2 

(1851) 143-. 
Fraction and quotient, fusion of notions. 

Bobynin, V. V. Bb. Mth. (1899) 81-. 
Fractions, compound, simplification. Euler, L. 

[1779] St Pet. Ac. Sc. Mm. 1 (1803-6) 3-. 
, elementary theory. Meray, C. , & Riquier, C. 

N. A. Mth. 8 (1889) 421-. 
, estimation. Petrie, W. M. F. [1875] Nt. 

13 (1876) 127-. 

with numerator 1, theorems. Fuss, N. 
[1809] St Pet. Ac. Sc. Mm. 10 (1826) 27-. 

of 1, conversion to decimals. De Morgan, 
A. Assur. Mg. 11 (*1864) 53-. 

, theorem. Posnikov, M. V. Kazan S. Nt. 

(Ps.-Mth.) P. 4 (1886) 238. 
, transformation. Lagrange, J. L. Par. EC. 

Pol. J. 2 (1798) (5 e cah.) 93-. 
, . Penjon, . Gergonne A. Mth. 4 

(1813-14) 265-. 
, into decimals. Arndt, J. A. Grunert 

Arch. 1 (1841) 101. 
, . Dienger, J. Grunert Arch. 11 

(1848) 232. 

' ar, expansion in sorites. Sylvester, 

J. J.' Am. J. Mth. 3 (1880) 332-, 388-. 
, , reduced to decimal, number of figures. 

Sornin, J. N. A. Mth. 8 (1849) 50-. 
Frolov's groups of numbers. Studnicka, F. J. 

Casopis 19 (1890) 124- ; Fschr. Mth. (1890) 

196. 
Functions obtained by combining the four 

fundamental operations. Bianchi, G. Pa- 

lomba Eac. 2 (1846) 326-. 
Geometry, generalisation of arithmetical opera- 
tions in reference to. Wiegand, A. Mathe- 
matician 3 (1850) 60-. 
G. C. M. Finck, B. N. A. Mth. 1 (1842) 

353-. 
. Bertrand, J. N. A. Mth. 8 (1849) 

358-. 
. Gordan, P. [1873] Mth. A. 7 (1874) 

433-. 

. Gegenbauer, L. Wien Ak. Sb. 91 

(1885) (Ab. 2) 333-. 

, abridged method of finding. Nieven- 

gloski, G. H. N. A. Mth. 8 (1849) 447-. 

, Lame's theorem. Finck, B. N. A. 

Mth. 4 (1845) 71-. 

and L. C. M. Gergmme, J. D. Ger- 
gonne A. Mth. 21 (1830-31) 117-. 

. Barrieu, P. (xn) Ma- 
thesis 3 (1883) 217- ; N. A. Mth. 14 (1895) 
95-, 165-, 214-. 

, mean values. Cesaro, E. A. Mt. 13 

(1885) 235-. 

, new method. Binet, J. P. M. C. B. 

13 (1841) 349-. 

, number of divisions. Lame,G. C.B. 

19 (1844) 867-. 

, . Binet, J. P. M. C. B. 19 

(1844) 937-. 

, . Nievengloski, G. H. N. A. 

Mth. 4 (1845) 568-. 



44 



0410 



Rational Numbers; Arithmetical Operations 



0410 



G. C. M., number of divisions. Lionnet, E. 

N. A. Mth. 4 (1845) 617- . 
, . Dupre, A. Liouv. J. Mth. 

11 (1846) 41-. 
, . Grunert, J. A. Grunert 

Arch. 8 (1846) 137-. 
, . Schulten, N. G. af (fil.). 

Helsingf . Acta 2 (1847) (pte. 2) 745-. 
, . Lionnet, E, N. A. Mth. 



10 (1851) 85-. 
, Poinsot's method. Grunert, J. A. 

Grunert Arch. 7 (1846) 153-. 
of two numbers, expression for. 

Lerch, M. Prag Sb. (1885) (Mth.-Nt.) 414-. 



Harmonic series, property that (2m)! M?- 

is divisible by 2m + 1. Schiappa Monteiro, 

A. Lisb. J. Sc. Mth. 5 (1898) 224-. 
Imaginary bases for arithmetical notation. 

Griimwald, V. Brescia At. Cm. (1886) 

43-. 
Involution and evolution, improvements. 

Nicholson, P. Tilloch Ph. Mg. 52 (1818) 

341- ; 57 (1821) 33-. 
--- by logarithms, general rule. Eiddell, 

J. L. Silliman J. 7 (1849) 232-. 
Laisant's theorem on 1, 2, 3 ... (n- 1) in scale 

of notation n. Sokolow, N. Fschr. Mth. 

(1896) 141. 
Mental arithmetic. Cuthbertson, C. Nt. 45 

(1892) 78-. 
-- . Haas, K. Nt. 45 (1892) 198-. 

arithmetical feats by Inaudi, report on. 
Darboux, J. G. C. E. 114 (1892) 1335-. 

multiplication. Oakes, (Lieut.-Col.) W. H. 
Assur. Mg. 10 (*1863) 326-. 

, process. Saussure, H. de. Laus. Bll. 
S. Vd. 3 (1849-53) 256-. 

Multiplication, abridged, proof. Pedersen, H.A. 
Mth. Ts. 2 (I860) 50-. 

, , Thoyer's method. Cauchy, A. L. 
C. E. 12 (1841) 242-, 941-. 

, , various means. Gergonne, J. D. Ger- 
gonne A. Mth. 7 (1816-17) 157-. 

, arithmetical note. Scott, C. A. Science 
12 (1900) 648-. 

, commutative law in. Poussou [non Possou], 
. Mntp. Eec. Bll. 2 (1805) 252-. 

and division, numerical. Querret, . Ger- 
gonne A. Mth. 13 (1822-23) 277-. 

games, Lucas's " Arithmetique amusante" 
in particular. Studnicka, F. J. Casopis 25 
(1896) 289-; Fschr. Mth. (1896) 122. 

of numbers, facts concerning. Azoulay, . 
Par. S. Phlm. Bll. 4 (1892) 71-. 

--- , problem. Berg, F. J. van den. N. 
Arch. Wisk. 5 (*1879) 47-; 10 (1884) 202. 

by quarter squares. Laundy, S. L. Assur. 
Mg. 6 (*1857) 121-. 

rules, nature and teaching. Baron, R. 
Ens. Mth. 1 (1899) 317-. 

simplified by negative digits. Cunningham, 
A. Nt. 48 (1893) 316. 

, various kinds. Grassmann, H. Crelle J. 
49 (1855) 123-. 

Negative figures, arithmetic with. Longchamps, 
G. de. As. Fr. C. E. (1893) (Ft. 2) 200-. 



Nomography (helps in calculation) and need 
for its introduction in teaching. Pasquier, E. 
Ens. Mth. 1 (1899) 350-. 

Numbers, problems in theory. Gelin, E. Ma- 
thesis 16 (1896) (Suppl.) 34 pp. 

, property depending on scale of their nota- 
tion. Andreini,A. G. Mt. 26 (1888) 315- ; 
28 (1890) 43. 

, . Gambioli, . 

G. Mt. 27 (1889) 334-. 

, . Maillet, E. As. Fr. 

C. E. (1894) (Pt. 2) 242-. 

, . Gambioli, D. 

G. Mt. 33 (1895) 157-. 

Powers, formation, and root extraction. 
Querret, . Gergonne A. Mth. 12 (1821- 
22) 359-; 13 (1822-23) 163-. 

of integers. Mariantoni, F. Mathesis 18 
(1898) 244-. 

Proportion, problems. Lucchesini, . C. E. 

11 (1840) 476-. 
Pseudo-symmetric numbers. Lemoine, E. Par. 

S. Mth. Bll. 12 (1884) 155-. 
Pythagorean triangles. Safford, T. H. Wise. 

Ac. T. 12 (1900) 505-. 
Eeciprocals of numbers, theorems. Caminati, 

. As. Fr. C. E. (1887) (Pt. 1) 173. 
, table, construction. Lehmann, J. W. H, 

As. Nr. 52 (1860) 1-. 
Eoot extraction, new method. Gy'dry, S. (xn) 

Mag. Ak. Ets. (1850) 260- ; (1851) 57-, 

173-. 

, . Vazquez Prada, M. C. E. 121 

(1895) 635-. 

Eule of double-false-position. Poussou [non 
Possou], . Mntp. Eec. Bll. 3 (1809) 
285-. 



Scales of Notation. 

Berndtson, B. Stockh. Ac. Hndl. 39 (1818) 

212-. 
best number for radix. Thiele, T. N. Kjtfb. 

Ov. (1889) 25-. 
binary and octonary. Berdelle, C. As. Fr. C. 

E. (1887) (Pt. 2) 206-. 
, theorems. Simony, O. Mth. A. 31 (1888) 

549-. 
denary. Oettinger, L. Grunert Arch. 26 

(1856) 445-. 
, divisibility. Singer, E. Mil. G. I. Lomb. 

5 (1853) 141-. 
, . Hann, J. [1876] Z. Mth. Ps. 22 

(1877) 54-. 
, , criteria. Ziige, . Arch. Mth. Ps. 17 

(1900) 45-. 
, , two rules. Vervaet, P. J. Casopis 5 

(*1876) 189- ; Fschr. Mth. (1876) 84. 
division, arithmetical. Fontes, . As. Fr. 

C. E. (1892) (Pt. 2) 182- ; Toul. Ac. Sc. Mm. 

4 (1892) 289-. 
method of transformation. Barlow, P. 

Nicholson J. 25 (1810) 181-. 
with negative base. Grunwald, V. G. Mt. 23 

(1885) 203-, 367. 
number with digits reversed. Lemoine, E. 

As. Fr. C. E. (1883) 113-. 



45 



0410 Scales of Notation 

number with digits reversed, problem. Laisant, 
C. A. Bordeaux S. Sc. Mm. 1 (1876) 403-. 

, theorem. Lemoine, E. As. Fr. 

C. E. (1884) (Pt. 2) 58-. 

recurring digits, theorem. Glaisher, 
J. W. L. [1875] Mess. Mth. 5 (1876) 3-. 

whose powers terminate in same digits. 
Tanner, H. W. L. [1877] Mess. Mth. 7 
(1878) 63-. 

square ends in same digits as itself. 
Pabnstrom, A. Christiania Skr. (Mth.-Nt. 
Kl.) (1900) No. 3, 16 pp. 

12345679, properties. Plateau, J. A. F. 
(vm) Brux. Ac. Bll. 16 (1863) 62-. 

, (Plateau). Hooton, J. J. Intell. 
Obs. 4 (1864) 439. 

. , . Plateau, J. A. F. Brux. Ac. Bll. 

38 (1874) 469-. 
, , and generalisation. Laisant, G. A, 

Lisb. J. Sc. Mth. 5 (1898) 203-. 
octonary. Johnson, W. W. [1891] N. Y. 

Mth. S. Bll. 1 (1892) 1-. 
, application to system of weights and 

measures. Taylor, A. B. Am. Ph. S. P. 

24 (1887) 296-. 
powers of integers. Drot, . N. A. Mth. 4 

(1845) 637- ; 5 (1846) 25-. 
. Schlomilch, 0. Z. Mth. Ps. 12 

(1867) 350. 
. Andre, D. N. A. Mth. 16 (1877) 

370-. 
problems. Berdelle, C. As. Fr. C. E. (1898) 

(Pt. 2) 139-. 
quinary, denary, and vicenary. Marre, A. 

Liouv. J. Mth. 13 (1848) 233-. 
sum of digits. Berton, . N. A. Mth. 18 

(1859) 209-. 
of certain numbers. Sanctis, P. de. 

Em. N. Line. At. 46 (1893) 115-, 183- ; 47 

(1894) 53-; 50 (1897) 11-; 54 (1901) 18-. 
numbers, last. Gelin, (I'Abbe) . 

Les Mondes 43 (1877) 430-. 
sum of three consecutive numbers. 

Egidi, G. Em. N. Line. At. 46 (1893) 63-. 
sums of digits, numbers. Terrot, C. H. [1843] 

Edinb. E. S. T. (1849) 87-. 
theorem. Crelle, A. L. Crelle J. 30 (1846) 

215-. 
theorems. Sanctis, P. de. Em. N. Line. 

Mm. 11 (1895) 145-. 
"Tonal system." Nystrom, J. W. Franklin 

I. J. 46 (1863) 263-, 337-, 402-. 
2n-ary. Studnicka, F. J. Prag Sb. (1896) 

(Mth.-Nt.) No,. 7, 10 pp. 
with variable base. Sokolow, N. Fschr. Mth. 

(1896) 122. 
weights problem. Sornin, J. Toul. Mm. Ac. 

6 (1856) 37-. 
. Stahlberger, E. Carl Epm. 5 (1869) 

. F., E. R. Nt. 42 (1890) 568. 

. Willis, J. Nt. 43 (1891) 30-, 198. 

. Everett, J. D. Nt. 43 (1891) 104, 

199. 

. Macmahon, P. A. Nt. 43 (1891) 
113-. 

. B., E. E. Nt. 43 (1891) 198-. 



Irrational Numbers 0420 

weights problem, analogues. Matter, H. F. 
Z. Mth. Ps. 21 (1876) 227-. 

Square of large number. Pastorcek, J. M. 
Casopis 6 (*1877) 277-; Fschr. Mth. (*1877) 
808-. 

property of 48 ... 89, analogous numbers. 
Laisant, C. A. Par. S. Phlm. Bll. 4 (1892) 
77-. 

Sum or difference of products of factors. 
Austin, J. [1815] Am. Ph. S. T. 1 (1818) 
181-. 

Transformation of product of natural num- 
bers. Frisiani, P. Mil. Effem. As. (1850) 
44-. 

"Unitation," new arithmetical operation. 
Walenn, W. H. Ph. Mg. 36 (1868) 346-; 
46 (1873) 36-; 49 (1875) 346-; 50 (1875) 
117-, 521- ; 1 (1876) 546-; 4 (1877) 375-; 
5 (1878) 214- ; 9 (1880) 121-, 271-. 

0420 Existence of irrational and 
transcendental numbers; infinite 
processes adapted to rational 
numbers. 

Agreement of two methods of approximation to 

a square root (Newton & Lagrange). Carrara, 

B. G. Mt. 28 (1890) 39-. 
Algorithm for the calculation of the nth root 

of a. Schmidt, C. Mth. A. 45 (1894) 301-. 
Approximate evolution, note. Tanner, H.W.L. 

L. Mth. S. P. 23 (1892) 295-. 

representation of irrationals by rational 
fractions. Hurwitz, A. Mth. A. 39 (1891) 
279-. 

roots of numbers. Philbrick, . Iowa Ac. 
Sc. P. (* 1875-80) 24. 

and quotients, errors. Anon, (vi 546) 
Gergonne A. Mth. 13 (1822-23) 175-. 

Approximation by rational fractions. Hurwitz, 

A. Mth. A. 44 (1894) 417-. 
Archimedes and v '3. Thiele, T. N. Ts. Mth. 

2 (1884) 151- ; Fschr. Mth. (1884) 8. 
Arithmetic, transcendental. Eisenstein, G. 

Crelle J. 29 (1845) 177-. 
Arithmetical theorems, four. Strnad, A. Ca- 
sopis 17 (1888) 204- ; Fschr. Mth. (1888) 

185. 
Arithmetization of mathematics. Pierpont, J. 

N. Y. Am. Mth. S. Bll. 5 (1899) 394-. 
Chuquet, N., extraction of square root, 1484. 

Tannery, P. Bb. Mth. (1887) 17-. 
Chuquet's work, mean rule. Mansion, P. 

Bb. Mth. (1888) 36. 
Comparison of magnitudes ; Brouncker's method 

extended. Sang, E. [1870-90] Edinb. E. 

S. T. 26 (1872) 59-; Edinb. E. S. P. 18 

(1892) 341-. 
Continued radicals. Bouche,A. M.-et-L. Mm. 

S. Ac. 12 (1862) 81-. 
Convergents to the roots of a number. Muir, T. 

Edinb. E. S. P. 19 (1893) 15-. 
Cube, duplication with any approximation. 

Popov, A. T. (xii) Kazan Un. Mm. 6 (1871) 

233-. 



0420 Irrational Numbers 

Cube, duplication, new geometrical relation 
serving to solution of problem. Buonofalce, 
G. Les Mondes 41 (1876) 338-. 

root of 2, computation. Martin, Art. [1877] 
Mess. Mth. 7 (1878) 50-. 

, value to 28 places. Gray, P. 
Mess. Mth. 5 (1876) 172-. 

, verification and extension of 
value. Gray, P. [1877] Mess. Mth. 7 
(1878) 51-. 

roots of binomials, extraction. Lockhart, J. 
Thomson A. Ph. 6 (1815) 152-. 

(Lockhart). Horner, W. G. 

Thomson A. Ph. 8 (1816) 279-, 388-. 
Decimals, non-terminating, property. Young, 

J. R. Ph. Mg. 36 (1850) 15-. 
, periodicity. Looff, W. Grunert Arch. 16 

(1851) 54-. 
, recurring. Adams, Jas. Thomson A. Ph. 

2 (1821) 16-. 
, . Catalan, E. C. N. A. Mth. 1 (1842) 

457-. 
, . Stammer, W. Grunert Arch. 27 (1856) 

123-. 
, . Hansted, B. (xn) Ts. Mth. 2 (1878) 

180-. 
, . Glaisher, J. W. L. B. A. Rp. (1878) 

471- ; Nt. 19 (1879) 208- . 
, . Schlomilch, 0. X. Z. Mth. Ps. 25 

(1880) 416. 
, , class. Bouniakowsky, V. St Pet. Ac. 

Sc. Bll. 27 (1881) 362-. 
, , divisibility. Gamier, F. P. Moigno 

Cosmos 6 (1855) 238-. 
, , for -A-, general case for any radix. 

Glaisher, J. W. L. Mess. Mth. 2 (1873) 

188. 
, , and Henry Goodwyn's tables. Glaisher, 

J. W. L. [1878] Camb. Ph. S. P. 3 (1880 

185-. 
, , mixed, theory. Broda, K. [1874] 

Arch. Mth. Ps. 57 (1875) 297-. 
, , new properties. Coninck G. N. A. 

Mth. 13 (1874) 569-. 
, , periods. Dienger, J. Crelle J. 39 

(1850) 67-. 
, , property (Colling). Oliver, J. E. 

Camb. (M.) Mth. M. 1 (1859) 345-. 
, , theory. Sturm, J. B. Grunert Arch. 

33 (1859) 94-. 
, , . Broda, K. Arch. Mth. Ps. 56 

(1874) 85-. 
, theorem. Hansted, B. G. Teix. J. Sc. 2 

(1880) 154- . 

Equation x m =a + b,J -1. Valat, . Bor- 
deaux Act. Ac. Sc. (1844) 177-. 
Euclid, Book X, summary. Peano, G. Ev. 

Mt. 2 (1892) 7-. 
Fractions approximating to square root of a 

variable. Cebysev, P. St Pet. Ac. Sc. Mm. 

(Rs.) 61 (1890) (Suppl.) No. 1, 22 pp. ; Acta 

Mth. 18 (1894) 113-. 
, periodic. Laisant, G. A. Bordeaux S. 

Sc. Mm. 3 (1880) 213-. 
, , in given systems of numbers, law of 

formation. Broda, K. Arch. Mth. Ps. 68 

(1882) 85-. 



Irrational Numbers 0420 

Fractions, periodic, laws. Moret-Blanc, . 

N. A. Mth. 14 (1875) 229-. 
, , means of finding period. Laisant, A. 

Les Mondes 19 (1869) 331-. , 
, , properties. Beaujeux, E., <& Laisant, A. 

N. A. Mth. 7 (1868) 289-. 
, , theorems. Thibault, . N. A. Mth. 2 

(1843) 80-. 

Incommensurability , general theorem. Maizwre, 

de. Gergonne A. Mth. 1 (1810-11) 

293-. 
, and its treatment in certain books. 

Amicis, E. de. Rv. Mt. 5 (1895) 110-. 
Incommensurable fraction, development. 

Young, J. R. Ph. Mg. 36 (1850) 128-. 

lines. Lebesgue, V. A. N. A. Mth. 3 

(1844) 436-. 

, \/3 : 1. Bretschneider, C. A. Grunert 
Arch. 3 (1843) 440-. 

number, meaning to be attached to the term, 
etc. Meray, C. Par. EC. Norm. A. 4 
(1887) 341-. 

numbers. Wantzel, L. Par. EC. Pol. J. 15 
(1837) (25 e cah.) 151-. 

. of algebraic origin. Wantzel, L. N. A. 
Mth. 2 (1843) 117- ; Par S. Phlm. P.-V. (1843) 
10-. 

, general remarks. Girault, . Rouen 

Tr. Ac. (1849-50) 96-. 
1 geometrical proof of theorem. Sylvester, 

J. J. (xn) J. H. Un. Cir. [1] (1882) 179-, 

209. 

and limits. Jablonski, E. N. A. 
Mth. 20 (1881) 241-. 

, property. Stephanos, G. Par. S. Mth. 

Bll. 7 (1879) 81-. v 

, theorem of Cebysev. Le Paige, C. 
Brux. Ac. Bll. 25 (1893) 235-. 

quantities. Leger, E. Liouv. J. Mth. 1 
(1836) 93-. 

, elementary theory. Egidi, G. Rm. N. 

Line. At. 46 (1893) 149-. 

, theorem. Lebesgue, V. A. Liouv. J. 
Mth. 1 (1836) 266-. 

roots and logarithms, definitions. Guilmin, 

A. N. A. Mth. 6 (1847) 313-. 
Irrational formulae, irreducible. Bouniakowsky, 

V. [1840] St Pet. Ac. Sc. Mm. 4 (1841) 

471-. 

. , reciprocals. Canter zani, S. Bologna 
Mm. I. It. 1 (pte. 2) (1806) 301-. 

numbers. Minnigerode, B. Mth. A. 4 
(1871) 497-. 

. Peano, G. Rv. Mth. 6 (1896-99) 126-. 

, arithmetical properties. Ghristoffel, 
E. B. A. Mt. 15 (1887-88) 253-. 

, definition. Illigens, E. Mth. A. 35 

(1890) 451-. 

development in rational continued 
fractions. Schulten, N. G. af (fil.) [1847] 
Helsingf. Acta 3 (1852) 405- . 

, introduction. Pasch, M. Mth. A. 40 

(1892) 149-. 
, , with method of contiguous classes. 

Capelli, A. G. Mt. 35 (1897) 209-. 
, theorems. Ramsay, A. Stockh. 6fv. 

39 (1882) No. 9, 21-. 



47 



0420 Irrational Numbers 

Irrational numbers, theory. Dantscher von 
Kollesberg, V. Innsb. Nt. Md. B. 17 (1887) 

, Weierstrass-Cantor theory. Illigens, E. 

Mth. A. 33 (1889) 155- . 

quantities, approximate determination, two 
methods. Giinther, S. Erlang. Ps. Md. S. 
Sb. 6 (1874) 82-. 

, equidifferent multiples. Sang,E. [1880] 

Edinb. E. S. P. 11 (1882) 2-. 
Irrationality, arithmetical. Glaisher, J. W. L. 

Ph. Mg. 45 (1873) 191-. 

of cos , except when n=l, 2, 3, 4 or 6. 

Wendt, C. Mh. Mth. Ps. 10 (1899) 97-. 
Irrationals, algebraic, theory. Capelli, A. 

Nap. Ed. 30 (1891) 61-. 
Limit-value and irrational numbers. Jensen, 

J. L. W. V. Ts. Mth. 3 (1885) 33-; Fschr. 

Mth. (1885) 203. 
Limits and irrational numbers, theory. Arzela, 

C. (xn) Ev. Sc.-Ind. 10 (1878) 77-, 144-, 

177-. 

Periods of decimals equivalent to 1/p, termina- 
tor. Sardi, C. [1868] G. Mt. 7 (1869) 24-. 
for Jv, il?, -&, etc., short process. 

Glaisher, J. W. L. Mess. Mth. 7 (1878) 

190-. 
Pythagorean series for side and diagonal of 

square. Hultsch, F. Bb. Mth. 1 (1900) 8-. 
Eadicals, calculation. Eggers, H. Des Moines 

Anal. 3 (1876) 100-. 
, extraction, general method. Ruffini, P. 

[1812] Mod. S. It. Mm. 16 (1813) 373-; 

17 (1815) 1-. 
, quadratic, approximate value. Poncelet, 

J. V. Crelle J. 13 (1835) 277-. 
, , values. Horvath, . (xn) Mag. 

Tud. Ak. Ets. 1 (No. 8) (1867) 150- ; (x) Par. 

S. Phlm. Bll. 4 (1867) 247-. 
, , approximation, Poncelet's theorem. 

Zeuner, G. Schlomilch Z. 3 (1858) 383-. 
, , Poncelet's approximate linear valuation. 

Sylvester, J. J. Ph. Mg. 20 (1860) 203-. 
, , geometric approximation. LeauU, 

H. Par. S. Mth. Bll. 8 (1880) 106-. 
, , theorem, extension to trinomial. 

Eesal,H.A. (xi) Par. S. Mth. Bll. 1 (1873) 

, , theorems for linear representation 

generalised. Sylvester, J. J. B. A. Ep. 

(1860) (pt. 2) 7. 
Eeal numbers, theory of, according to 

Dedekind's conception. Eicci, G. Ven. I. 

At. (1892-93) 233- ; G. Mt. 35 (1897) 22-. 
Eoot extraction. West, B. Bost. Mm. Am. 

Ac. 1 (1785) 165-. 
. Anon, (vi 782) Madrid Ev. 2 (1851) 

. Kinkelin, H. Grunert Arch. 26 (1856) 

361-. 
. Evans, A. Des Moines Anal. 3 (1876) 

. Chokrobarthy,S.N. Edinb. Mth. S. P. 

16 (1898) 77. 
, approximate. Dienger, J. Grunert 

Arch. 17 (1851) 421-. 



Irrational Numbers 0420 

Eoot extraction, approximate. Heaton, JEf. 
A. Mth. 1 (1884-85) 14-. 

, cubic, &c. Young, M. Ir. Ac. T. 1 

(1787) 59-. 

of fractions, Ampere's method; applica- 
tion to gamut. Vincent, A. J. H. N. A. 
Mth. 5 (1846) 5-. 

of integers by binomial theorem. 
Martin, Art. Des Moines Anal. 1 [1874] 117-. 

, nth degree. Eggers, H. Des Moines 

Anal. 2 (1875) 14-. 
Eoots of all powers, extraction. Hoare, C. 

Franklin I. J. 39 (I860) 50-. 
, approximate calculation, and applications. 

Thallmayer, V. Arch. Mth. Ps. 10 (1891) 

32-. 
, formulae for calculation. Borgogelli, M. 

Em. N. Line. At. 45 (1892J 101-. 
, expression by rational fractions. Thiele, 

T. N. N. Ts. Mth. 1 (B) (1890) 33- ; Fschr. 

Mth. (1890) 221-. 
, higher, extraction. Greene, D. Camb. 

(M.^Mth. M. 1 (1859) 123-. 

'HjN, last n figures by division. Anne, J/. 
N. A. Mth. 4 (1845) 561-. 

, numerical, extraction, abridged. Bobillier, 
. Gergonne A. Mth. 20 (1829-30) 125-. 

and powers, calculation. Cordeiro-Feyo, J. 
Lisb. Mm. Ac. Sc. 12 (1837) (pte. 1) 1-. 

, rapid method of approximation. Collins, 
M. B. A. Ep. 42 (1872) (Sect.) 13-. 

Square and cube root extraction, abridged. 
Finck, B. N. A. Mth. 5 (1846) 250-. 

, degree of approximation. 
Verhulst, P. F. N. A. Mth. 7 (1848) 46-. 

roots. Fitremann, . N. A. Mth. 

10 (1871) 87-. 
, rules for contracting processes, 

incorrectness of. Hill, M. J. M. L. Mth. 

S. P. 18 (1886-87) 171-. 

other roots, principal values. Tilly, 
de. Mathesis 15 (1895) 177-, 217- ; 16 
(1896) 5-. 

root extraction. Crosson, A. N. A. Mth. 5 
(1846) 128- . 

. Alexeeff, N. Par. S. Mth. Bll. 7 

(1879) 167-. 
. Darboux, G. Bll. Sc. Mth. 11 

(1887) 176-. 
. Pavlov, A. P. Kazan S. Nt. (Ps.- 

Mth.) P. 6 (1888) 8. 

. Bougon, . Ev. Sc. 46 (1890) 283-. 

. Kleiber, J. Ev. Sc. 46 (1890) 507-. 

, abridged. Catalan, E. C. N. A. 

Mth. 17 (1858) 232-. 
, . Hill, M. J. M. B. A. Ep. 

(1886) 538. 
, . Raffalli, J. Ev. Sc. 47 (1891) 

90-. 
, . Decamps, A. Ev. Sc. 50 (1892) 

764. 
, , history. Cantor, M. N. A. Mth. 

20 (1861) 46-. 
, methods. Grunert, J. A. Grunert 

Arch. 30 (1858) 275-. 
, rapidly converging series for. Muir, 

T. Edinb. E. S. P. 17 (1891) 14-. 



48 



0430 Aggregates 

Square root of polynomial, approximate frac- 
tions. Alekseev, N. St Pet. Ac. Sc. Mm. 
(Rs.) 37 (*1881) 107-. 

2 and of 3, approximations. Henry, C. 

Bll. Sc. Mth. As. 3 (1879) 515-. 

roots, approximate expressions for. Hauber, 
C. F. Lindenau Z. 4 (1817) 95-. 

of numbers. Weill, . Par. S. Mth. 

Bll. 14 (1886) 128-. 
Surd, formula for fraction approximate in 

value. Whitworth, W. A. [1874] Mess. 

Mth. 4 (1875) 79-. 
Surds and irrationals, classification. Baker, 

A. L. Rochester (N.Y.) Ac. Sc. P. 2 (1895) 

202-. 

, expansion. Adams, Jas. Thomson 

v-w 

A. Ph. 16 (1820) 418-. 

0430 Aggregates. 

Absolute convergence of improper integrals, 
explanation. Stolz, O. Wien Ak. Sb. 107 
(1898) (Ab. 2o) 207- ; 108 (1899) (Ab. 2a) 
1234-. 

Aggregate question in billiards. Vivanti, G. 
Ev. Mt. 5 (1895) 87-. 

Aggregates of aggregates. Burali-Forti, C. 
Mth. A. 47 (1896) 20-. 

, extension of enumerable. Garibaldi, C. 
Palermo Cir. Mt. Ed. 8 (1894) 157-. 

formed by special values of a function. 
Schmifliess, A . Konigsb. Schr. 41 (1900) [11]-. 

, foundations of general theory. Cantor, G. 

Acta Mth. 2 (1883) 381-. 
, functional. Arzela, C. Bologna Ac. Sc. 

Mm. 5 (1895-96) 225- ; 8 (1899-1900) 131-. 

and incommensurable numbers. Amigues, 
E. Mars. Fac. Sc. A. 2 (1892) 33-. 

of points, and their signification for analysis. 
Lerch, M. Casopis 15 (1886) 211- ; Fschr. 
Mth. (1886) 194-. 

, single valued (eindeutig) and continuous 
formation. Jtirgens, E. D. Nf. Tbl. (*1878) 

, theory. Cantor, G. [1877] Crelle J. Mth. 

84 (1878) 242-. 

, . Netto,E. Crelle J. Mth. 86 (1879) 263-. 
, . Baire, R. C. E. 129 (1899) 946-. 
, , auxiliary theorem. Bendixscm, I. 

Stockh. Ak. Hndl. Bh. 9 (1884-85) No. 7, 

7 pp. 
, , basis. Gruithuisen, F. von P. 

Gruithuisen N. Analekt. 1 (1834) (Heft 3) 

1- ; (Heft 4) 1- ; (Heft 6) 45-. 
, , elementary point in. Cantor, G. D. 

Mth. Vr. Jbr. 1 (1892) 75-. 
, , history and bibliography. Vivanti, G. 

Bb. Mth. (1892) 9-. 
, , note. Tannery, P. Par. S. Mth. Bll. 

12 (1884) 90-. 
, , . Garibaldi, C. Palermo Cir. Mt. 

Ed. 9 (1895) 198- . 
Algebra, foundations. Ascoli, G, Mil. I. 

Lomb. Ed. 28 (1895) 1060-. 
Analytic functions. Vivanti, G. Palermo Cir. 

Mt. Ed. 3 (1889) 38-. 

VOL. I. 



Aggregates 0430 

Analytic functions, a property of. Poincare, H, 
Palermo Cir. Mt. Ed. 2 (1888) 197-. 

representation of real functions, given over 
any aggregate of points. Phragmen, E. 
Palermo Cir. Mt. Ed. 14 (1900) 256-. 

Asymptotic arithmetic, contribution to funda- 
mental principles of. Cesaro, E. Nap. Ac. 
At. 6 (1894) No. 11, 23 pp. 

Behaviour of certain functions at infinite 
values of variables. Vivanti, G. Palermo 
Cir. Mt. Ed. 2 (1888) 135-, 150-. 

Boundaries of continua. Phragmen, E. Acta 
Mth. 7 (1885) 43-. 

Cantor, a theorem of. Burali-Forti, C. Tor. 
Ac. Sc. At. 32 (1896) 153- or 229-. 

Cantor's theorems. Schroder, E. D. Mth. 
Vr. Jbr. 5 (1901) (Heft 1) 81-. 

Commensurable quantities, distribution. 
Cesaro, E. A. Mt. 13 (1885) 295-. 

Condensation of singularities, Hankel and 
Dini's principle. Krtpke, . Hamb. Mth. 
Gs. Mt. 1 (1889) 230-. 

Construction of tangents to circles and limit- 
circles ; proof that Lobatschef sky's space 
contains a doubly infinite manifoldness of 
spheres of infinite radius. Simon, M. D. 
Mth. Vr. Jbr. 3 (1894) 80-. 

Continuity of functions. Pincherle, S. Bologna 
Ed. 4 (1900) 99-. 

inconsistent with one to one correspondence 
between different spaces. Milesi, L. Ev. 
Mt. 2 (1892) 103-. 

Continuous aggregate, ?i-fold, conception. 
Jiirgens, E. D. Mth. Vr. Jbr. 7 (Heft 1) 

(1899) 50-. 

aggregates, theorem. Cantor, G. Gott. Nr. 
(1879) 127-. 

and connected aggregates. Maccaferri, E. 
Ev. Mt. 4 (1894) 97-. 

function with discontinuous differential 
coefficient. Lerch, M. G. Teix. J. Sc. 9 
(1889) 97-. 

Convergence conditions. Fouret, G. N. A. 

Mth. 9 (1890) 222-. 
. Giudice, . Palermo Cir. Mt. Ed. 4 

(1890} 284-. 
"Crinkly" curves (i.e. filling a surface). 

Moore, E. H. N. Y. Am. Mth. S. T. 1 

(1900) 72-, 507. 

Definition of magnitudes 0, 1, 2, 3. Schroder, 

E. Ac. Nt. C. N. Acta 71 (1898) 363-. 
real number. Burali-Forti, C. [1900] 

N. Y. Am. Mth. S. Bll. 7 (1901) 158, 

170-. 
Differentiable function oscillating in every 

interval. Kopcke, A. Hamb. Mth. Gs. Mt. 

2 (1890) (Festschr. Tl. 2) 128-. 
Discontinuities of functions of real variable. 

Bettazzi, E. Palermo Cir. Mt. Ed. 6 (1892) 

173-. 
Finite classes. Burali-Forti, C. Tor. Ac. Sc. 

At. 32 (1896) 34-. 

and infinite assemblage. Keyser, C. J. 
[1900] N. Y. Am. Mth. S. Bll. 7 (1901) 
218-. 

Finiteness, two definitions of, and Cantor's 
theorems. Schroder, E. Ac. Nt. C. N. Acta 
71 (1898) 301-. 



49 



0430 Aggregates 

Function with symmetries in every interval. 

Kopcke, A. [1896] Hamb. Mth. Gs. Mt. 3 

(1900) 258-. 
Functions and aggregates, theory. Levi, B. 

Em. E. Ac. Line. Ed. 9 (1900) (Sem. 2) 72-. 

capable of graphic representation and 
differentiation. Kopcke, A. Hamb. Mth. 
Gs. Mt. 1 (1889) 128-. 

discontinuous in every interval. Peano, G. 
Ev. Mt. 2 (1892) 41-. 

oscillating in every interval, theorem. 
Kopcke, A. [1899] Hamb. Mth. Gs. Mt. 3 
(1900) 376-. 

Infinite numbers, various opinions. Cantor, 
G. Stockh. Ak. Hndl. Bh. 11 (1887) No. 19, 
10pp. 

, , Cantor's article. Enestrom, G. 

Stockh. Ofv. (1885) No. 10, 69-. 

series, convergence conditions. Giudice, . 
Palermo Cir. Mt. Ed. 4 (1890) 275-, 276-, 
278-, 279-, 280-, 281-, 283-. 

Infinitesimal constant segments, impossibility. 
Peano, G. Ev. Mt. 2 (1892) 58-. 

segments, remarks on a demonstration. 
Veronese, G. Palermo Cir. Mt. Ed. 6 (1892) 
73-. 

Integrability of ordinary differential equations. 

Arzela, C. Bologna Ac. Sc. Mm. 5 (1895- 

96) 257-. 
Integrals of ordinary differential equations, 

existence of. Arzela, C. Bologna Ac. Sc. 

Mm. 6 (1896-97) 131-. 
Limit, existence for regular sequences of 

rational numbers. Chessin, A. S. J. H. 

Un. Cir. [15 (1895-96)] 37-. 

of variable classes. Burali-Forti, C. Tor. 
Ac. Sc. At. 30 (1895) 227-. 

Limiting value of quotient series. Broden, T. 

[1897] Stockh. Ak. Hndl. Bh. 23 (Afd. 1) 

(1898) No. 2, 49 pp. 
Linear manifoldness in n dimensions. Amodeo, 

F. Ev. Mt. 2 (1892) 145-. 
Lines composed of rectilinear parts. Grave, D. 

C. E. 127 (1898) 1005-. 

Number, role of, in geometry. Calinon, A. 

[1900] N. Y. Am. Mth. S. Bll. 7 (1901) 158, 

178-. 
Ordered classes and transfinite numbers. 

Burali-Forti, C. Palermo Cir. Mt. Ed. 8 

(1894) 169-. 

types, theory. Vivanti, G. A. Mt. 17 
(1889-90) 1-. 

Perfect aggregates. Vivanti, G. Palermo Cir. 

Mt. Ed. 13 (1899) 86-. 
Point-aggregate, doubly extended, determination 

of all groups. Lie, M. S. Arch. Mth. Ntvd. 

3 (1878) 93-. 

aggregates. Phragmen, E. Stockh. Ofv. 

(1884) No. 1, 121-. 

, contents of. Harnack, A. Mth. A. 25 

(1885) 241-. 

, development of theory. Schoenfiies, A. 

D. Mth. Vr. Jbr. 8 (1900) (Heft 2) vi + 251 pp. 
, infinite, linear. Cantor, G. Mth. A. 

15 (1879) 1-; 17 (1880) 355-; 20 (1882) 
113- ; 21 (1883) 51-, 545-. 

, limiting values. Stolz, 0. Mth. A. 23 

(1884) 152-. 



Universal Algebra 0800 

Point aggregates, perfect, power of. Cantor, 

G. Acta Mth. 4 (1884) 381-. 
, , . Bendixson, I. Stockh. Ak. 



Hndl. Bh. 9 (1884-85) tfo. 6, 15 

in a plane. 

(Mth.-Nt.) 176-. 



in a plane. Lerc'h, M. Prag Sb. (1884) 



in space of n dimensions, theory. Cantor, 

G. Acta Mth. 7 (1885) 105-. 
, theorems. Bendixson, I. Acta Mth. 2 

(1883) 415-. 
Popular account of new fields of mathematics. 

Miller, G. A. Science 11 (1900) 528-. 
Quadratic aggregates in higher space. Sommer, 

J. D. Mth. Vr. Jbr. 8 (1900) (Heft 1) 193-. 
Eepresentation, uniform and continuous, of 

aggregates of different dimensions upon one 

another. Liiroth, J. Erlang. Ps. Md. S. 

Sb. 10 (1878) 190-. 
Segments and transfinite numbers. Veronese, 

G. Em. E. Ac. Line. Ed. 7 (1898) (Sem. 1) 

79-. 
Series, positive terms, partial sums forming 

continuum. Bettazzi, E. Tor. Ac. Sc. At. 

33 (1897) 199- or 355-. 
Subfinite and transfinite numbers from Cantor's 

point of view. Giudice, . Palermo Cir. 

Mt. Ed. 6 (1892) 161-. 
Successions. Giudice, . Palermo Cir. Mt. 

Ed. 5 (1891) 280-. 
Surfaces, general theory, extension to theory 

of aggregates. Mahler, . D. Nf. Tbl. 

(*1882) 147-. 
Transfinite magnitudes, class of. Janssen van 

Raay, W. H. L. G. Mt. 32 (1894) 1- ; 33 

(1895) 329-, 360. 
, theory. Cantor, G. Mth. A. 46 (1895) 

481- ; 49(1897)207-. 

numbers. Cantor, G. Ev. Mt. 5 (1895) 104-. 

. Stolz, 0. Ev. Mt. 5 (1895) 166-. 

. Killing, W. Mth. A. 48 (1897) 425-. 

. Levi-Civita, T. Em. E. Ac. Line. Ed. 

7 (1898) (Sem. 1) 91-, 113-. 

, Archimedes' axiom and projective 
geometry. Schonfiies, A. D. Mth. Vr. Jbr. 
5 (1901) (Heft 1) 75-. 

, question on. Burali-Forti, C. Palermo 

Cir. Mt. Ed. 11 (1897) 154-, 260. 

, Veronese's. ScMenflies, A. Em. E. 
Ac. Line. Ed. 6 (1897) (Sem. 2) 362-. 

Weierstrass-Cantor condensation process. 
Broden, T. Stockh. Ofv. (1896) 583-. 

Universal Algebra. 
0800 General. 

Algebra, foundation ; triple algebra. DeMorgan, 
A. (ix) [1844] Camb. Ph. S. P. 1 (1866) 13-. 

, notion and boundaries. Cayley, A. QJ. 
Mth. 6 (1864) 382-. 

, principles, fundamental. Macfarlane, A. 
Am. As. P. (1899) 21-. 

as science of pure time. Hamilton, (Sir) 
W. R. [1835] Ir. Ac. T. 17 (1837) 293-. 

Algebraic operations, philosophic deduction. 
Valente do Couto, M. Lisb. Mm. Ac. Sc. 3 
(pte. 2) (1814) 149-. 



50 



0800 Universal Algebra 

Algebraical fundamental operations, generalisa- 
tions. Simony, 0. Wien Ak. Sb. 91 (1885) 

(Ab. 2) 223-. 
Associative algebra, applicable to hyperspace. 

Joly, C. J. Ir. Ac. P. 5 (1898-1900) 73-. 
Calculus of notations. Couto, M. V. do, e 

Simoes Margiochi, F. Lisb. Mm. Ac. Sc. 

3 (pte 2) (1814) 48-. 
. Travassos, F. de P. Lisb. Mm. Ac. 

Sc. 3 (pte 2) (1814) 65-. 
Double algebra. Cayley, A. L. Mth. S. P. 15 

(* 1883-84) 185-. 
Factorials, calculus. Logan, H. F. C. [1873] 

E. S. P. 22 (1873-74) 434-. 
Generalisations of algebra. Spottisicoode, W. 

[1872] L. Mth. S. P. 4 (1871-73) 147-. 
Imaginaries in geometry, and tetrads, von 

Staudt's theory, and its extension. Liiroth, J. 

[1874-76] Mth. A. 8 (1875) 145- ; 11 (1877) 

84-. 
Laws of Motion, three, in world of universal 

algebra. Sylvester, J. J. (xn) [1883] J. H. 

Un. Cir. [3] (1884) 33-, 57. 
Linear algebra, uses and transformations. 

Peirce, B. Am. Ac. P. 10 (1875) 395-. 

associative algebra. Peirce, B. [1870] Am. 
J. Mth. 4 (1881) 97-. 

, note on Peirce's. Cayley, A, J. H. 

Un. Cir. [3] (1884) 122. 
Multiple algebra. Gibbs, J. W. Am. As. P. 

(1886) 37-. 

. Cayley, A. QJ. Mth. 22 (1887) 270-. 

, application of logical analysis. Peirce, 

C. S. Am. Ac. P. 10 (1875) 392-. 

algebras, class. Peirce, C. S. (xn) [1882] 
J. H. Un. Cir. [2] (1883) 3-. 

Negative numbers. Burali-Forti, C. Ev. Mt. 
3 (1893) 138-. 

quantities. Flauti, V. [1855] Nap. At. Ac. 
(1855-57) 3-. 

, addition, Bertrand. Terquem, 0. (vi 

Adds.) N. A. Mth. 15 (1856) 172-. 
, conception. Purgotti, S. Palomba Eac. 

3 (1847) 171-, 180-. 

and rule of signs. Guillon, E. L. N. A. 

Mth. 8 (1849) 28-. 
, theory. Cach, . Gergonne A. Mth. 4 

(1813-14) 1-. 
, . Gergonne, J. D. Gergonne A. Mth. 

4 (1813-14) 6-. 

, . Transon, A. (Prof.). N. A. Mth. 3 

(1844) 318-, 321-. 
. US e. Prouhet, E. N. A. Mth. 6 (1867) 

337-. 
Physics, algebra of, principles. Macfarlane, A. 

Am. As. P. (1891) 65-. 
Postulates of algebra. Padoa, [1900] N. Y. 

Am. Mth. S. Bll. 7 (1901) 70. 
Proportion, theory. Lehmann, J. W. H. 

Grunert Arch. 8 (1846) 113-. 
Signs of operation, distributed, in systems of 

algebra. Graves, C. Ir. Ac. P. 3 (1847) 325-. 
Sylvester's third law of motion, proof. Buch- 

heim, A. Ph. Mg. 18 (1884) 459-. 
Symbolical algebra. Gregory, D. F. [1838] 

Edinb. E. S. T. 14 (1840) 208-. 
. Vanecek,M.N. Prag Sb. (1888) (Mth.- 

Nt.) 137-. 



Calculus of Operations 0810 

Symbols, algebraic, and tessarines. Cockle, Jas. 

Ph. Mg. 34 (1849) 406- . 
Tessarines, amplitude. Cockle, Jas. Ph. Mg. 

36 (1850) 290-. 
Tetrads (Wiirfe) theory. Liiroth, J. Gott. Nr. 

(1873) 767-. 

( ) von Staudt's theory. Sturm, R. Mth. 

A. 9 (1876) 333-. 

( ), . Schroder, E. Mth. A. 10 

(1876) 289-. 

Universal algebra. Brunei, . Bordeaux S. 
Sc. Mm. 2 (1891) ix-. 

, principles. Sylvester, J. J. Am. J. 
Mth. 6 (1884) 270-. 

0810 Calculus of Operations. 

Algebra of multilinear partial differential opera- 
tors. MacMahon, P. A. L. Mth. S. P. 19 
(1889) 112-. 

Algebraical operation. Cayley, A. QJ. Mth. 
13 (1875) 369-. 

(repeated) transformation, principle. Scha- 
pira, H. Heidi. Nt. Md. Vh. 4 (1892) 25-. 

Calculus of chemical operations. Brodie, (Sir) 

B. C. Phil. Trans. 156 (1866) 781-. 
. Williamson, A. W. C. N. 16 

(1867) 3-. 
. Brodie, (Sir) B. C. [1876] Phil. 

Trans. 167 (1877) 35-. 
, Brodie's. Naquet, A. Ph. Mg. 7 

(1879) 418-. 
functions. Babbage, C. [1815-20] Phil. 

Trans. (1815) 389-; (1816) 179^; (1817) 197- ; 

QJ. Sc. 2 (1817) 371- ; Camb. Ph. S. T. 1 

(1822) 63-. 
. Tanner, H. W. L. Mess. Mth. 7 

(1878) 156- . 
, Babbage's paradox. Graves, J. T. 

Ph. Mg. 9 (1836) 334-, 443-. 
of one independent variable. Liventsov, 

A. I. (xn) [1875] Eec. Mth. (Moscou) 8 
(1876) (Pt. 1) 80-. 

linear partial differential operations. 
MacMahon, P. A. QJ. Mth. 24 (1890) 246-. 

, the most comprehensive. Schroder, E. 

B. A. Ep. (1883) 411-. 

of operation symbols, elementary exposition. 
Cazzaniga, P. G. Mt. 20 (1882) 48-, 194-. 

operations. Boole, G. Phil. Trans. 

(1844) 225-. 

. Graves, C. Ph. Mg. 34 (1849) 60-. 

. Paterson, J. Silliman J. 11 (1851) 

327-. 
, application to algebraic expansions. 

Hargreave, C. J. Ph. Mg. 6 (1853) 351-. 
, to transformation of trigonometric 

series. Donkin, W. F. QJ. Mth. 3 (1860) 

, development. Roberts, S. QJ. Mth. 

4 (1861) 44-. 

extended form of index symbol. 
Spottiswoode, W. Phil. Trans. (1860) 13-. 

, formula*. Stokes, G. G. [1876] 

Edinb. B. S. P. 9 (1878) 101-. 
, , general. Spottiswoode, W. Crelle 

J. 59 (1861) 367-. 

51 D2 



0810 Calculus of Operations 

Calculus of operations, notes. Studnicka, F. 

Prag Sb. (1871) (pt. 2) 39-. 
, problem. Westergaard, H. (xn) Ts. 

Mth. 6 (1876) 37-. 

, supplement. Paterson, J. [1874] 
Alb. I. T. 8 (1876) 191-. 

, theorem. Walton, W. QJ. Mth. 3 

(1860), 278-, 314-. 
, and applications. Greer, H. R. 

QJ. Mth. 3 (1860) 148-. 
, , note. Roberts, S. QJ. Mth. 3 

(1860) 310-. 
, theorems. Donkin, W. F. Camb. 

and Dubl. Mth. J. 5 (1850) 10-. ' 
, . Spottiswoode, W. Camb. and 

Dubl. Mth. J. 8 (1853) 25-. 

, . Carmichael, R. Camb. and 
Dubl. Mth. J. 8 (1853) 165-. 

; . Crofton, M. W. QJ. Mth. 16 

(1879) 323-. 
, . Walker, J. J. [1880-81] 

L. Mth. S. P. 11 (1879-80), 108- ; 12 

(1880-81) 193-. 
, , general, and applications. Warren, 

J. W. [1861] QJ. Mth. 5 (1862) 29-. 
symbols. Spottiswoode, W. Phil. Trans. 

(1862) 99-. 
, applications to differential equations. 

Russell, W. H. L. Phil. Trans. (1861) 69- ; 

(1862) 253- ; (1863) 517-. 
, to non-linear differential equations. 

Russell, W. H. L. E. S. P. 13 (1864) 423-. 
, to partial differential equations. 

Russell, W. H. L. E. S. P. 13 (1864) 432-. 

, division, internal and external. 
Spratt, T. A. B. E. S. P. 11 (1860-62) 
557-. 

, recent discoveries. Russell, W. H. L. 

B. A. Kp. (1862) (pt. 2) 7-. 
Complete system of polar mutually permutative 

operations. Gapelli, A. Nap. Ed. 32 (1893) 

29-, 155-. 

De Morgan's extension of the algebraic pro- 
cesses (symbolic algebra). Ladd, C. Am. 

J. Mth. 3 (1880) 210-. 
Determinants, Smith's. Mansion, P. (xn) 

Brux. S. Sc. A. 2 (1878) (Pt. 2) 211-. 
Differentials of symbolic expressions. Lipschitz , 

R. Berl. Ak. Sb. (1899) 122-. 
Differentiation with fractional indices, and 

differentiation, general. Center, W. Camb. 

and Dubl. Mth. J. 3 (1848) 274-; 4 (1849) 

21-; 5 (1850) 206-. 

generalised. Moritz, R. E. N. Y. Am. 
Mth. S. Bll. 6 (1900) 184, 185-. 

Distributive functional calculus. Pincherle, S. 

Mil. I. Lomb. Ed. 30 (1897) 1031- ; Mth. A. 

49 (1897) 325-. 
operations. Pincherle, S. Em. E. Ac. 

Line. Ed. 4 (1895) (Sem. 1) 142-. 
. Calo, B. Em. E. Ac. Line. Ed. 4 

(1895) (Sem. 2) 52-. 

operations differing by permutation from a 
given operation. Pincherle, S. Tor. Ac. 
Sc. At. 30 (1895) 820-. 

Divisibility by a polynomial, extension of the 
conception. Pincherle, S. Em. E. Ac. 
Line. Ed. 7 (1898) (Sem. 1) 185-. 



Calculus of Operations 0810 

Equations analogous to differential equations. 

Bourlet, C. C. E. 124 (1897) 1431-. 
. Appell, P. C. E. 124 (1897) 

1433-. 
Exponential formula giving sum of sines or 

cosines of angles in arithmetical progression. 

Horta, F. Lisb. A. 1 (1857) 713-. 

symbolic operators, theorems. Glaisher, 
J. W. L. QJ. Mth. 15 (1878) 266-. 

Exponentials, representation of function. 01- 
tramare, G. Sch. Nf. Gs. Vh. (1896) 50-. 

Fractional power of (-j--\ x' } . Center, W. 

Camb. and Dubl. Mth. J. 3 (1848) 163-. 
Functional equations, replacement of arbitrary 
constants by operative symbols. Tanner, 
H. W. L. Mess. Mth. 7 (1878) 157- ; 8 (1879) 
13. 

operations, certain. Pincherle, S. Bologna 
Ac. Sc. Mm. 7 (1886) 393-. 

, groups. Levi-Civita, T. Mil. I. Lomb. 

Ed. 28 (1895) 458-, 864-. 
, , and the inversion of definite integrals. 

Levi-Civita, T. Mil. I. Lomb. Ed. 28 (1895) 

529-, 565-. 
Functions, determination by formal conditions. 

Schroder, E. Crelle J. Mth. 90 (1881) 189-. 
, symbolic representations. Bronwin, B. 

Camb. and Dubl. Mth. J. 2 (1847) 134-. 
General algorithms and iteration. Lemeray, . 

C. E. 126 (1898) 510- ; Par. S. Mth. Bll. 26 

(1898) 10-. 
Hyperdistributives. Cockle, (Sir) J. Ph. Mg. 

43 (1872) 300-. 
Integration problems. Rubini, R. G. Mt. 19 

(1881) 118-. 
Iteration. Bourlet, C. C. E. 126 (1898) 583-. 

of functions. Aristov, I. I. Kazan S. Ps.- 
Mth. Bll. 10 (1901) 14-, 85-; Fschr. Mth. 
(1900) 403-. 

, the problem. Bourlet, C. Toul. Fac. Sc. 

A. 12 (1898) c, 12 pp. 
, . Lemeray, . C. E. 128 (1899) 

278-, 380. 
Iterative calculus, principles. Bottcher, . E. 

Prace Mt.-Fiz. 10 (1899-1900) 65-. 
Laplace's transformation. Amaldi, U. Em. E. 

Ac. Line. Ed. 7 (1898) (Sem. 2) 117-. 
Law of combination of operators. Campbell, 

J. E. [1897] L. Mth. S. P. 29 (1898) 14-. 
Mathematical operations, especially restricted 

differentiation. Gruenewald, . D. Nf. Tbl. 

(*1868) 130-. 

Multiplication of functional distributive opera- 
tions. Bortolotti, E. Em. E. Ac. Line. 

Ed. 7 (1898) (Sem. 1) 16-. 
partial differential operators. Sylvester, 

J. J. Ph. Mg. 33 (1867) 48-. 
Notation, "representative." Blissard, J. [1862] 

QJ. Mth. 6 (1863) 49-. 
0, a certain differential, determinantal operator. 

Vivanti, G. Palermo Cir. Mt. Ed. 4 (1890) 

261-. 
Operation on functions, definition [<f>n(x) for 

<f> (x) repeated n times, where n is fractional]. 

Appell, P. Par. S. Phlm. Bll. 3 (1879) 

166. 



52 



0810 Calculus of Operations 

Operation, laws. Ellis, A. J. E. S. P. 10 

(1859-60) 85-. 
Operations equivalent to their adjuncts. Bor- 

tolotti, E. Em. E. Ac. Line. Ed. 7 (1898) 

(Sem. 2) 74-. 

in general. Bourlet, C. C. E. 124 (1897) 
348-. 

, remarkable sequence. Brunei, G. Bordeaux 

S. Sc. P.-V. (1896-97) 86-. 
, theorems. Grolous, J. Par. S. Phlm. Bll. 

12 (1875) 81-. 
Periodicity, generalisation of notion. Brunei, . 

Bordeaux S. Sc. Mm. 4 (1888) xxvi-. 
Quotient- and product-calculation. Guldberg, 

A. S. Ts. Mth. 2 (1884) 84-, 161- ; Fschr. 

Mth. (1884) 342. 
Eeduction of Cayley 's operation to polar 

operations. Capelli, A. Mth. A. 29 (1887) 

331-. 
Signs + and , nature in symbolical algebra. 

Gregory, D. F. Camb. Mth. J. 3 (1843) 153-. 
Symbolic calculus, principles. Cesdro, E. (xn) 

Mathesis 3 (1883) 10-. 

equation, Tr m ir n u + qpu = 0, where symbols 
""m' ""n) P combine according to the laws 

"K-mP = pTT m +l ' ' Jr m' n 'n = lr n' lr m, + a ( n ~ m ) P' 

Boole, G. Camb. and Dubl. Mth. J. 2 
(1847) 7-. 

equations, certain. Piiicherle, S. Bologna 
Ac. Sc. Mm. 5 (1895-96) 663-. 

, employment. Cauchy, A. L. C. E. 
17 (1843) 449-. 

, interchange of symbols. Graves, C. 
Ir. Ac. P. 6 (1853-54) 144-. 

, resolution of non-linear. Cauchy, A. L. 

C. E. 22 (1846) 235-. 
, theorems and formulae deduced from. 

Cauchy, A. L. C. E. 17 (1843) 377-. 

expansions. Russell, W. H. L. E. S. P. 
14 (1865) 329-. 

methods, proofs of (1) formula for nth 
differential coefficient, (2) Euler's theorems 
on quantics, (3) Staudt's theorem on Ber- 
noulli's numbers. BuchJieim, A. Mess. 
Mth. 11 (1882) 143-. 

relations 



&c. Johnson, W. W. Mess. Mth. 11 (1882) 
191-. 

theorem involving repeated differentiations. 
Glaisher, J. W. L. [1879] Camb. Ph. S. P. 
3 (1880) 269-. 

theorems, Crofton. Glaisher, J. W. L. 
QJ. Mth. 16 (1879) 257-. 

variability of several dimensions. Formenti, 
C. Mil. I. Lomb. Ed. 16 (1883) 288-, 351-. 

versus operative expansion. Hathaway, 
A. S. Des Moines Anal. 5 (1878) 38-. 

Symbolical expression, properties and applica- 
tion to attraction of ellipsoid. Cayley, A. 
Camb. Mth. J. 3 (1843) 62-. 

Symbols of operation. Crofton, M. W. Am. 
J. Mth. 4 (1881) 269-. 



Complex Numbers 0820 

Symbols, relation of certain. Cockle, (Sir) J. 

[1879] QJ. Mth. 17 (1881) 20-, 208-. 
Ternary quadric operators on products of forms 

of any orders. Walker, J. J. L. Mth. S. P. 

20 (1889) 110-. 
Transmutations. Bourlet, C. Par. S. Mth. 

Bll. 25 (1897) 132-. 
Uniform substitutions and Babbage's problem. 

Iaggi,E. N. A. Mth. 19 (1900) 483-. 
, convergence. Lemeray, E. M. N. A. 

Mth. 16 (1897) 306- ; 17 (1898) 75-. 

regarded as function of n. Krug, A. 



Wien. Ak. D. 57 (1890) 151-. 

0820 General theory of complex 
numbers. (See also 2870.) 

d'Alembert's equation 

(1 + W^T) m = (1 - h x/^T)" 1 . 

Cossali, P. [1783] Mod. Mm. S. It. 9 (1802) 

231-. 
Algebraic couples. Hamilton, (Sir) W. R. 

[1835] Ir. Ac. T. 17 (1837) 293-. 

. Cayley, A. Ph. Mg. 27 (1845) 38-. 

. Hargreave, C. J. B. A. Ep. (1857) 

184-. 

equations, theory. Gegenbauer, L. Mh. 
Mth. Ps. 6 (1895) 12-. 

integers. Landsberg, G. D. Mth. Vr. Jbr. 
4 (1897) 111-. 

numbers, new foundation for theory. 
Hensel, K. D. Mth. Vr. Jbr. 6 (1899) 
(Heft 1) 83-. 

and transcendent equations, complex num- 
bers derived from. Hug, J. C. Zur. Vjschr. 
7 (1862) 270-. 

triplets. Graves, C. Ir. Ac. P. 3 (1847) 
51-, 57-, 80-, 105-. 

Calculation with p + qj-l. Ohm, M. D. 

Nf. Vsm. B. (1845) 73-. 
Chessboard, mathematical theory. Problem of 

n queens on board of n 2 spaces. Giinther, S. 

Arch. Mth. Ps. 56 (1874) 281-. 
Complex and bicomplex numbers, theory. 

Benthem, A. Arch. N6erl. 12 (1877) 

113-. 

coordinates in plane geometry. Berlin, M. 
Lund. Acta Un. 9 (1872) (Mth.) No. 4, 
45 pp. 

elements in analytical geometry, significance. 
Stolz, 0. Mth. A. 4 (1871) 416-. 

factors. Cauchy, A. L. C. E. 24 (1847) 
347-. 

forms, real representations. Segre, C. 
Mth. A. 40 (1892) 413- . 

geometry, contribution. Sforza, G. Q. Mt. 
30 (1892) 159-. 

integers. Lanavicensis (Sylvester, J. J.). 
QJ. Mth. 4 (1861) 94-, 124-. 

magnitudes, addition-logarithms for. 
Mehmke, R. Z. Mth. Ps. 40 (1895) 15-. 

number, cosine, significance in plane geo- 
metry. Thiele, T. N. (xn) Ts. Mth. & 
(1876) 177-. 



53 



0820 



General theory of complex numbers 



j. 



Complex numbers. Genocchi, A. Liou 

Mth. 19 (1854) 281-. 

. Pad, P. G. Mt. 11 (1873) 244-. 

. Zolotarev, E. I. [1877] St. Pet. Ac. 

Sc. Bll. 24 (1878) 310-. 

, analysis. Denzler, W. Ziir. Mt. 3 
(1853-55) 560-. 

, with application to equation ar x + j/ A =2\ 

Kummer, E. E. Berl. Ab. (1857) (Mth.) 

, application to n dimensions. Mollame, V. 

G. Mt. 31 (1893) 271-. 
comprised in formula a + b *j c. Pepin, 

T. Liouv. J. Mth. 1 (1875) 317-. 

, elementary theory. Hoiiel, J. Bor- 
deaux Mm. S. Sc. 5 (1867) 1- ; 6 (1868) 1- ; 
8 (1870) 97-; 1 (1876) 1-. 

formed from roots of unity. Kummer, 
E. E. Liouv. J. Mth. 12 (1847) 185- ; 
16 (1851) 377-; Berl. Mb. (1861) 1051- ; 
(1863) 21-. 

. Kronecker, L. Berl. 

Mb. (1863) 340-. 

. Fuchs, L. [1864] 

Crelle J. 65 (1866) 74-. 

, prime factors. Kummer, 
E. E. Crelle J. 35 (1847) 327-. 

and 2nd factor of class 
number. Kummer, E. E. Berl. Mb. (1870) 
855-. 

, simplest representation. 

Kummer, E. E. Berl. Mb. (1870) 409-. 

w n = l, ideal prime factors. 

Kummer, E. E. Berl. Ab. (1856) (Mth.) 1-. 

Xth roots of unity. Kummer, E. E. 

Crelle J. 40 (1850) 93-, 117-. 

31st roots of unity. Kummer, E. E. 

Berl. Mb. (1870) 755-. 
, Gaussian representation of. Breuer, A. 

Arch. Mth. Ps. 12 (1894) 337-. 
geometric representation of a new kind. 

Kotelinikov, A. P. Kazan S. Ps.-Mth. Bll. 

6 (1896) (Prot.) 26. 
, significance (Schlomilch). Unfer- 

dinger, F. Arch. Mth. Ps. 52 (1871) 252-. 
, introduction. Baltzer, R. [1882] Crelle 

J. Mth. 94 (1883) 87-. 
, mechanical interpretation. Zbikovskij, 

A. K. Kazan S. Nt. (Ps.-Mth.) P. 6 (1888) 6. 

, multiplication, geometric significance. 
Orelli, J. Ziir. Vjschr. 20 (1875) 443-. 

, new method for graphical representation. 

Brill, J. Mess. Mth. 17 (1888) 80-. 
and their functions, theory. Hertz, K., 

& Dicksttin, S. Par. T. Nauk Sc. Pam. 7 

(*1875) Art. 3, 60 pp. 
, theorem of Dedekind, proof. Study, E. 

Gott. Nr. (1898) 1-. 
, theory. Lejeune-Dirichlet, G. Berl. 

Ab. (1841) 141-. 
, . Kummer, E. E. Berl. B. (1846) 

87-; Crelle J. 35 (1847) 319-. 
, . Wantzel, L. C. B. 24 (1847) 

430-. 
, . Bachmann, P. Crelle J. 67 (1867) 

, . Dedekind, E. C. B. 90 (1880) 1205-. 



0820 



Complex numbers, theory. Zolotarev, E. J. 
Liouv. J. Mth. 6 (1880) 51-, 129-. 

units. Kronecker, L. [1845] Crelle J. 
Mth. 93 (1882) 1-. 

. Lejeune-Dirichlet, G. Berl. B. (1846) 

103-. 
. Kronecker, L. Crelle J. 53 (1857) 

176- ; C. B. 96 (1883) 93-, 148-, 216-. 
. Molk, J. Bll. Sc. Mth. As. 7 (1883) 

(Pt. 1) 133-. 
, addition to memoir on. Kronecker, L. 

C. B. 99 (1884) 765-. 

, expressions formed from. Kummer, 
E. E. Crelle J. 50 (1855) 212-. 

Conjugate functions and imaginary logarithms. 
Hamilton, (Sir) W. R. B. A. Ep. (1834) 
519-. 

Cube root of >Ja+ bi in form x + yi, simple solu- 
tion. Simony, O. Arch. Mth. Ps. 55 (1873) 
72-. 

roots, imaginary, number of (Lockhart). 
Homer, W. G. Thomson A. Ph. 8 (1816) 
279-, 388-. 

of unity, theorem of algebra, geometry 

deduced from. Appell, P. C. B. 84 (1877) 

540-. 
Directive numbers, theorems, and proof of 

Cauchy's theorem on closed contours. Tran- 

son, A. N. A. Mth. 7 (1868) 97-. 
Discriminants of finite ' ' fields. ' ' Dedekind, R. 

Gott. Ab. 29 (1882) Art. 2, 56 pp. 
Every equation in one unknown can be 

satisfied by a complex value of this un- 
known, geometric proof. Wittstein, T. 

Grunert Arch. 6 (1845) 225-. 
Format's theorem, generalization for Galois 

number fields. Moore, E. H. N. Y. Am. 

Mth. S. Bll. 2 (1896) 189-. 
G. C. M. of 2 complex numbers, number of 

divisions. Dupre, A. Liouv. J. Mth. 13 

(1848) 333-. 

Geometrical representation of \/-l, considera- 
tion of objections. Warren, J". Phil. Trans. 

(1829) 241-. 
Goniometry, application of principles given by 

Warren. Terrot, C. H. [1847] Edinb. B. 

S. T. 16 (1849) 345-. 
Imaginaries. Buee, . [1805] Phil. Trans. 

(1806) 23-. 
. Fran^ais, J. F. Gergonne A. Mth. 4 

(1813-14) 222-, 364-. 

. Volpicelli, P. G. Arcad. 52 (1831) 221-. 
. Bellavitis, G. Poligrafo 5 (1831) 15-; 12 

(1832) 211-. 

. Arenstein, J. Haidinger B. 3 (1847) 292-. 
. Bellavitis, G. Yen. At. 6 (1847) 459-; 

Yen. Mm. I. 4 (1852) 243-. 
. Arenstein, J. Haidinger Ab. 2 (1848) 

(Ab. 2) 43-. 

. Cockle, Jas. Ph. Mg. 36 (1850) 281-. 
. Grunert, J. A. Grunert Arch. 20 (1853) 

121-. 

. Sabatie, J. N. A. Mth. 2 (1863) 206-. 
. Cheyrezy, U. N. A. Mth. 3 (1864) 445-. 
. Sexe, S. A. N. Mg. Ntvd. 16 (1869) 1-; 

17 (1870) 233-; Arch. Mth. Ntvd. 7 (1882) 

115-. 



54 



0820 



General theory of complex numbers 



0820 



Imaginaries, d'Alembert's theorem. Du Bour- 

guet, . Gergonne A. Mth. 4 (1813-14) 20-. 
, . Gergonne, J. D. Gergonne A. Mth. 

4 (1813-14) 23-. 
, . Barsotti, G. Lucca At. Ac. 11 

(1842) 393-. 
in algebra. Janssen van Eaaij, W. H. L. 

Haarl. Ms. Teyl. Arch. 4 (1896) 53-. 
, application to mechanics. Durege, . 

Ziir. Vjschr. 7 (1862) 293-. 
, summation of trigonometric series, 

and calculation of integrals. Michaelis, J. P. 

Lux. S. Sc. Mm. 7 (1864) 172-. 
, theory of curves. Durege, H. Arch. 

Mth. Ps. 42 (1864) 1-. 
, bisignal univalent. Kirkman, T. P. Ph. 

Mg. 37 (1850) 292-. 
, Bolyai's theory. Stdckel, P. Mth. Termt. 

fits. 17 (1899) 259-; Mth. Nt. B. Ung. 16 

(1899) 263-. 
, calculation with, and geometrical theorems. 

Zech, P. Grunert Arch. 16 (1851) 354-. 
, calculus. Carmichael, E. Ph. Mg. 6 (1853) 

273-. 
, construction for. Cayley, A. Mess. Mth. 

10 (1881) 1-. 
, defective notation. Mathematicus.[Pseudon.~\ 

(vi Adds.) Nicholson J. 29 (1811) 254-; 31 

(1812) 193-. 
, doctrine. Walton, W. Camb. and Dubl. 

Mth. J. 8 (1853) 101-. 
, in coordinate geometry. Walton, W. 

Camb. and Dubl. Mth. J. 7 (1852) 234-. 
, employment in geometry. Laguerre, . 

N. A. Mth. 9 (1870) 163-, 241-. 
, of space. Laguerre, . N. A. 

Mth. 11 (1872) 14-, 108-, 241-. 
, Fresnel's interpretation. Lippich, F. 

Prag Sb. (1864) (Pt. 2) 73-. 
, geometric application. Schou, (Lieut.) 

T. V. (xn) Ts. Mth. 1 (1865) 129-. 
, construction. Drobisch, M. W. Leip. 

B. 2 (1848) 171-. 
, meaning. Zehfuss, G. Grunert Arch. 

32 (1859) 234-. 
, representation. Argand, . Gergonne 

A. Mth. 4 (1813-14) 133- ; 5 (1814-15) 

197-. 
, . Durege, . Ziir. Vjschr. 3 (1858) 

358. 
, . Lie, S. Crelle J. 70 (1869) 346- ; 

Christiania F. 22 (1870) 16-, 107-. 
, , applications to cubic equations, etc. 

Wittstein, T. Grunert Arch. 7 (1846) 402-. 
, significance of form a + 1) V - 1. Mutter, 

G. W. Grunert Arch. 1 (1841) 397-. 
(Grones). Toblini, G. Poligrafo 14 (1833) 

37-. 
, history of theory. Betnan, W. W, Am. 

As. P. (1897) 33-. 
, how to avoid. Sexe, S. A. Arch. Mth. 

Ntvd. 4 (1879) 145-. 
, , and elementary theory. Sexe, 

S. A. Arch. Mth. Ntvd. 9 (1884) 205-. 
, interpretation in mathematical physics. 

Chancaurtais, E. B. de. C. E. 68 (1869) 

127-. 



Imaginaries, new theory. Cauchy, A. L. C. 

E. 24 (1847) 1120-. 
, , various applications. Cauchy, A. L. 

C. E. 25 (1847) 129-. 
, octaves. Cayley, A. Ph. Mg. 30 (1847) 

257. 
, paradox resulting from employment. 

Mathematicus . [Pseudon.] (viAdds.) Nichol- 
son J. 30 (1812) 209-. 
, real sum of two, Lagrange's equation, 

proof. Plana, G. Tor. Mm. Ac. 16 (1857) 

97-. 
, reality. Matzka, W. Bohm. Gs. Ab. 6 

(1851) 179-. 

, relation of V - 1 to geometrical perpen- 
dicularity. Paterson, J. Am. As. P. (1851) 

1-. 
, representation, etc. Ballauff, L. Grunert 

Arch. 5 (1844) 259-. 
, , method. Duport, . Par. EC. Norm. 

A. 9 (1880) 301-. 
, , . Amstein, H. Laus. S. Vd. Bll. 18 

(1882) 1-. 
, , new. Duport, . C. E. 88 (1879) 

1071-. 
, simplification. Nordmark, Z. Ups. N. 

Acta S. Sc. 8 (1821) 136-. 
, 8-square. Cayley, A. [1882] Am. J. Mth. 

4 (1881) 293-. 
, . Sylvester, J. J. (xn) J. H. Un. 

Cir.Jl] (1882) 203. 
, <s/~l. Warner, H. S. Ph. Mg. 30 (1847) 

185. 

, . Guthrie, F. Ph. Mg. 39 (1870) 282-. 
, theory. Frangais, J. F. Gergonne A. 

Mth. 4 (1813-14 364-. 
, . Dirksen, E. H. Berl. B. (1839) 6-. 
, . Burhenne, H. Grunert Arch. 22 

(1854) 43-. 
, . Laurent, P. A. Par. EC. Pol. J. 23 

(1863) (40 e cah.) 75-. 
, . Berger, . [1864] Mntp. Mm. Ac. 

Sect. Sc. 6 (1864-66) 1-. 
_, _. Gomes Teixeira, F. (xn) Brux. S. Sc. 

A. 7 (1883) (Pt. 1) 59-, (Pt. 2) 417-. 
, (Teixeira). Mansion, P. (xn) Mathesis 

3 (1883) (Suppl.) 13-. 
, truth of conclusions obtained. Woodhouse, 

R. Phil. Trans. (1801) 89-. 
. , use in integral calculus. Stille, W. A. 

Des Moines Anal. 2 (1875) 33-. 
Imaginary of algebra. Macfarlane, A. Am. 

As. P. (1892) 33-. 

expressions and foreign solutions of equa- 
tions. Bourdat, . [1854] Grenoble Ac. 
Delph. Bll. 5 (1859) 121-. 

, limits of some. Tortolini, B. G. Arcad. 

87 (1841) 145-. 

forms; their interpretation. Valles, F. 
N. A. Mth. 9 (1870) 20-. 

and negative quantities, nature. Gilbert, D. 
[1830] Phil. Trans. (1831) 91-. 

, anew. Cockle, Jas. Ph. Mg. 34 (1849) 37-. 

numerical forms in geometry. Moth, F. X. 
Munch. Ab. 3 (1837-43) 85-. 

points in piano, a representation. Appell, P. 
Arch. Mth. Ps. 61 (1877) 359-. 



0820 Complex Numbers 

Imaginary powers of quantities, geometrical 
representation. Warren, J. Phil. Trans. 
(1829) 339-. _ 

e zkir *~ l , paradox. Catalan, E. C. 

N. A. Mth. 8 (1869) 456-. 

radicals, principle of fundamental substitu- 
tion in. Saporetti, A. Bologna Ed. (1878) 
126-. 

and real forms, contiguity in approximate 
solutions. Valles, F. N. A. Mth. 13 (1854) 
449-. 

Involution and evolution of imaginaries con- 
sidered geometrically. Henkle, W. D. Des 
Moines Anal. 1 (1874) 149-. 

Logarithms of negative quantities, and on 
imaginaries. Fontana, G. Verona S. It. 
Mm. 1 (1782) 183-. 

Numbers, irreducible with complex numbers. 
Formenti, C. Mil. I. Lomb. Ed. 16 (1883) 
981-. 

Partitions of complex numbers (theorem con- 
tained in theorem of Jacobi's). Sylvester, 
J. J. C. E. 96 (1883) 1276-. 

Position of chessmen defined by complex 
variables. Gochmann, C. Fschr. Mth. (1897) 
426. 

Power with complex base and exponent, 
geometrical representation. Durege, . 
Ziir. Vjschr. 5 (1860) 297-. 

Powers with imaginary exponents. Ballauff", L. 
Grunert Arch. 6 (1845) 409-. 

Prime factors, ideal, of complex numbers, 
formed rationally from roots of an irredu- 
cible equation. Selling, E. Z. Mth. Ps. 
10 (1865) 17-. 

Product of complex factors, reduction. Schiappa 
Monteiro, A. Lisb. J. Sc. Mth. 5 (1898) 
209-. 

Quadratic forms, number. Eisenstein, G. 
Crelle J. 27 (1844) 311-. 

, belonging to real determinant. 
Eisenstein, G. Crelle J. 27 (1844) 80. 

Quaternions, proof of Frobenius' theorem on 
their relation to complex numbers. Grisse- 
mann, F. X. Mh. Mth. Ps. 11 (1900) 132-. 

Eeality of quantities called imaginary, of form 
a + W-1, etc. Desmousseaiuc de Givre", 
F. X. E. Par. Ing. Civ. Mm. (1877) 389-. 

Eelative Abelian number-fields. Hilbert, D. 
Gott. Nr. (1898) 370-. 

. Wiman, A. Lund. Un. Acta 36 

(1900) (S. Psgr. No. 6) 17 pp. 

quadratic "fields" (Korper). Hilbert, D. 
[1897-99] D. Mth. Vr. Jbr. 6 (1899) (Heft 1) 
88-; Mth. A. 51 (1899) 1-. 

Boots of e 2 = -1. Plarr, G. Edinb. E. S. P. 

15 (1889) 93-. 
unity. Cayley, A. Mess. Mth. 4 (1875) 

171. 
Seventh roots of unity. Cayley, A. Mess. 

Mth. 7 (1878) 177-. 

Symbols, imaginary, geometrical interpreta- 
tion. Franqais, J. F. Gergonne A. Mth. 

4 (1813-14) 61-. 
Theory, means of extending without use of 

imaginaries. Saltel, L. C. B. 94 (1882) 

166-. 



Quaternions 0830 

Triangle, figure of, regarded as a complex 

quantity. Frege, G. [1878] Jena. Sb. (1879) 

xviii. 

Triple algebra and application to solid geo- 
metry. Graves, C. Ph. Mg. 34 (1849) 

119-. 
Triplets, functions of two variables employed in 

interpreting. Graves, C. Ir. Ac. P. 5 (1853) 

423-. 
Twenty -third roots of unity. Cayley, A. 

Crelle J. 55 (1858) 192; 56 (1859) 186-. 
Units in rationality domain of 5th roots of 1. 

Gmeiner, J. A. Mh. Mth. Ps. 9 (1898) 184-. 
Zero, imaginary and real. Eiccati, G. Verona 

S. It. Mm. 4 (1788) 116-. 
, . Fontana, G. [1798] Mod. S. It. 

Mm. 8 (1799) 174-. 
Zeros, imaginary. Young, J. R. Ph. Mg. 27 

(1845) 91-. 

0830 Quaternions. 

Analogue to quaternions in 4 dimensions. 

Wijthoff, W. A. Amst. Ak. Vs. 6 (1898) 

520-. 
Conditions of integrability of Suadp, Suftdp, 

Suydp, elimination of o, /3, 7 from. Plarr, 

G. [1874] Edinb. B. S. T. 27 (1876) 251-. 
Conjugate numbers in general, solution of 

quadratics by quaternions in particular. 

Studnicka, F. J. Casopis 23 (1894) 72-; 

Fschr. Mth. (1893-94) 149. 
Coordinates versus quaternions. Cayley, . 

Edinb. B. S. P. 20 (1895) 271-. 
Coplanarity and homoconicism, quaternion 

expressions. Spottiswoode, W. Ph. Mg. 36 

(1850) 379-. 
Curves cutting plane into squares, systems. 

Tail, P. G. Edinb. Mth. S. P. 7 (1889) 2-. 

of inversion. Raimondi, R. G. Mt. 26 
(1888) 181-. 

Determinants of quaternions. Peirce, <7. M. 

N. Y. Am. Mth. S. Bll. 5 (1899) 335-. 
Differentiation of power of a quaternion. 

M'Aulay, A. [1889] Edinb. E. S. P. 16 

(1890) 201-. 
. Note on M'Aulay's paper. 

Tait, . [1889] Edinb. E. S. P. 16 (1890) 

205-. 

in the quaternion analysis. MacFarlane, A. 
Ir. Ac. P. 6 (1900-02) 199-. 

Displacements, finite, of system of points 
whose mutual distances remain invariable; 
quaternion expression. Plarr, G. (xi) [1883] 
Edinb. E. S. P. 12 (1884) 151-. 

Dupin's theorem [on intersection lines of three 
systems of orthogonal surfaces] by quater- 
nions. Hamilton, (Sir) W. R. Ir. Ac. P. 6 
(1853-54) 86-. 

and its converse, geometrical proof. 
Sommerfeld, A. D. Mth. Vr. Jbr. 6 (1899) 
(Heft 1) 123-. 

Electrodynamics and magnetism, quaternion 
investigations. Tait, P. G. QJ. Mth. 3 
(1860) 331-. 

Elementary universal geometry, new terms. 
Sylvester, J. J. Nt. 32 (1885) 576-. 



56 



0830 Quaternions 

Ellipsoids, theorem. Hamilton, (Sir) W. R. 

Ir. Ac. P. 4 (1850) 349-. 
Equation Q = q (w, x, y, z) = w + ix +jy + kz. 

Spottiswoode, W. Ph. Mg. 36 (1850) 135-. 

Vp<pp 0, graphic solution. Tait, P. G. 
Edinb. E. S. P. 10 (1880) 400-. 

, in quaternions. Elfrinkhof, L. van. 
N. Arch. Wisk. 1 (1895) 76-; Fschr. Mth. 
(1893-94) 135. 

representing a linear vector function, 
generally not self -con jugate. Plarr, G. 
[1876] Edinb. E. S. T. 28 (1879) 45-. 

Equations in multiple quantity. Sylvester, 
J. J. Nt. 31 (1885) 35-. 

quaternions, solution of a class. 
Sylvester, J. J. Ph. Mg. 17 (1884) 392-. 

Finite quaternion groups, determination. 

Stringham, W. I. Am. J. Mth. 4 (1881) 

345-. 

Geometrical calculus, essay. Lasker, E. L. 

Mth. S. P. 28 (1897) 217-, 500-. 

interpretation of log Uq. Macfarlane, A. 
Ph. Mg. 38 (1894) 143-. 

Green's formula, application to the study of 

the electric field. Larose, H. A. Tel. 22 

(1895) 460-. 
Hamilton groups. Dedekind, R. Mth. A. 48 

(1897) 548-. 
. Miller, C. A. N. Y. Am. Mth. S. Bll. 

4 (1898) 510-. 
. D'Atonandro, A. G. Mt. 37 (1899) 

138-. 
Hamiltonian pairs, and generalized theory of 

complex variable. Maksimovich, V. P. (xn) 

[1883-84] Kazan S. Nt. (Ps.-Mth.) P. 2 

(1884) i-, 95-. 
Hamilton's equation in quaternions, explicit 

solution. Sylvester, J. J. C. E. 99 (1884) 

555-. 

method, attempt at new development. 
Dillner, G. [1876] Mth. A. 11. (1877) 168-. 

operator V, applications in calculus of 
variations. Joly, C. J. Ir. Ac. P. 5 (1898- 
1900) 666. 

quadrantal versors. Wettum, T. B. van. 
N. Arch. Wisk. 20 (1893) 1- ; Fschr. Mth. 
(1893-94) 225-. 

Homogeneous strains. Metzler, W. H. A. 

Mth. 8 (1893-94) 148-. 
Homographic divisions of planes, spheres and 

space (quaternion methods). Joly, C. J. 

Ir. Ac. P. 4 (1896-98) 515-. 
Hyperbolic quaternions. Macfarlane, A . [1900] 

Edinb. E. S. P. 23 (1902) 169-. 
Imaginary or uniaxal geometry, illustrations. 

Cockle, Jas. Ph. Mg. 34 (1849) 132-. 
Infinite and imaginary, use in service of finite 

and real. Sylvester, J. J. Nt. 32 (1885) 

103-, 271. 
Inverting a linear and quaternion function of a 

quaternion. Hamilton, (Sir) W. R. (m) 

[1862] Ir. Ac. P. 8 (1864) 182-. 
Laplace's equation, application of quaternions 

to. Brill, J. Camb. Ph. S. P. 7 (1892) 

120-, 151-. 
, quaternion integration. PreobraZenskij, 

V. V. Kazan S. Nt. (Ps.-Mth.) P. 2 (1884) 

46-; Fschr. Mth. (1884) 308-. 



Quaternions 0830 

Laplace's equation, quaternions. Carmichael, 
R. Ir. Ac. P. 6 (1853) 216-. 

Linear bilateral quaternion equation, geometri- 
cal interpretation. Stringham, I. Am. As. 
P. (1884) 54-. 

differential equations in quaternions. Tait, 
P. G. [1870] Edinb. B. S. P. 7 (1872) 
311. 

equation of quaternions, Hamilton's and the 
author's methods of solution. Sylvester, J. J. 
C. E. 99 (1884) 473-. 

, solution of general. Sylvester, J. J. 

C. E. 99 (1884) 502-. 

vector operator of quaternions. Shaw, J. B. 
Am. J. Mth. 19 (1897) 267-. 

Mechanics, applications of quaternions. Lais- 
ant, C. A. Liouv. J. Mth. 3 (1877) 
325-. 

, . Genty, . Liouv. J. Mth. 7 

(1881) 49-. 

by quaternions. Hyde, E. W. Des Moines 
Anal. 7 (1880) 137-, 177- ; 8 (1881) 17-, 
49-. 

Minding's theorem, quaternion investigations 
connected with. Tait, P. G. [1879] Edinb. 
E. S. P. 10 (1880) 200. 

, proof. Walker, J. J. L. Mth. S. P. 

10 (1878-79) 100-. 

, . Tait, P. G. L. Mth. S. P. 10 

(1878-79) 101-. 

Operations, theorem in. Tait, P. G. Edinb. 
Mth. S. P. 8 (1890) 21-. 

Operator <f> (V). Tait, P. G. Edinb. E. S. P. 
7 (1872) 607-. 

Point and line calculus, with special reference 
to parallels. Graefe, E. Arch. Mth. Ps. 15 
(1897) 34-, vii-. 

Potential of closed circuit, quaternion investi- 
gation. Tait, P. G. QJ. Mth. 4 (1861) 
143-. 

Problem of Fermat, to find point, sum of whose 
distances from 3 given points is least, solu- 
tion. Tait, P. G. [1867] Edinb. E. S. P. 6 
(1869) 165-. 

Quaternion analysis, geometrical proofs of 
theorems by. Hamilton, (Sir) W. R. Ir. Ac. 
P. 5 (1853) 407-. 

, new geometrical interpretation. Brill, J. 

Camb. Ph. S. P. 6 (1889) 156-. 

associative principle. Hathaway, A. 8. 
[1895] N. Y. Am. Mth. S. Bll. 2 (1896) 
43-. 

, definition. Christie, A. S. Wash. Ph. S. 
Bll. 11 (1892) 579-. 

differences, an equation in. Tait, P. G. 
Edinb. E. S. P. 12 (1884) 561-. 

differentiation. M'Aulay, A. [1890] Edinb. 
E. S. P. 18 (1892) 98-. 

equations, solution of a large class. 
Sylvester, J. J. C. E. 98 (1884) 651-. 

forms of propositions in fluid motion. 
Butcher, J. G. [1876] L. Mth. S. P. 8 
(1877) 174-. 

formulae. Allardice, R. E. Edinb. Mth. 
S. P. 7 (1889) 8-. 

for quantification of curves, surfaces and 

barycentres. Stringham, W. I. Am. J. 
Mth. 2 (1879) 205-. 



57 



0830 Quaternions 

Quaternion formulae for reduction of multiple 
integrals. Carvallo, E. Par. S. Mth. Bll. 
18 (1890) 80-. 

, function, development. Graves, C. Ir. 
Ac. P. 6 (1853-54) 385-. 

group, the. Miller, G. A. 
37 (1898) 312-. 

innovations. Heaviside, O. Nt. 49 (1893- 
94) 246. 

integrals, some. Tait, P. G. [1870] Edinb. 
E. S. P. 7 (1872) 318-, 784-. 

integration, a. Tait, P. G. [1871] Edinb. 
B. S. P. 7 (1872) 434-. 

, theorems in. McAulay, A. Mess. Mth. 

14 (1885) 26-. 

invariants of linear vector functions, and 
quaternion determinants. Joly, G. J. Ir. 
Ac. P. 4 (1896-98) 1-. 

and its depreciators. Knott, G. G. Edinb. 
Mth. S. P. 11 (1893) 62-. 

method, intrinsic nature of. Tait, P. G. 
[1894] Edinb. B. S. P. 20 (1895) 276-. 

note on a geometrical problem. Tait, 
P. G. [1889] Edinb. E. S. P. 16 (1890) 
315-. 

notes. Tait, P. G. Edinb. E. S. P. 15 
(1889) 379-. 

, from number to. Fleuri, G. N. S. W. 

E. S. J. 28 (1894) 65-. 
" Path," Tait's, note. Martin, H. [1867] 

Edinb. E. S. P. 6 (1869) 121-. 

proof of reciprocal curves in space. 
Hamilton, (Sir) W. B. B. A. Ep. (1862) 
(pt. 2) 4. 

Samuel Eoberts' theorem of 4 co- 
intersecting spheres. Walker, J. J. L. 
Mth. S. P. 12 (1880-81) 147-. 

- triple generation of three-bar 
motion. Hart, H. [1882] Mess. Mth. 12 
(1883) 32-. 

transformation, a. Tait, P. G. Edinb. E. 
S. P. 5 (1863) 115-. 

transformations. Tait, P. G. Edinb. E. 
S. P. 7 (1872) 501-. 

. Gwyther, R. F. Manch. Lt. Ph. S. 

P. 19 (1880) 118-. 

treatment of linear complex. Buchheim, A. 
Mess. Mth. 13 (1884) 120-. 

variables, functions. StudniCka, F. J. 
Prag Sb. (1894) (Mth.-Nt.) No. 26, 8 pp. 

Quaternions. Hamilton, (Sir) W. B. [1843 

Ir. Ac. T. 21 (1848) 199-. 
. Cayley, A. Ph. Mg. 26 (1845) 141-, 

208-. 
. Tait, P. G. Mess. Mth. 1 

140-, 203-. 
. Kelland, P. 
. Ladd, C. 

172-. 
. Stringham, W. I. 

310-. 
. Wood, De V. Des Moines Anal. 7 (1880) 

11-, 33-, 65-, 121-. 
. Christie, A. S. Des Moines Anal. 7 

(1880) 185-. 

. Ball, B. S. Nt. 48 (1893) 391. 
. Studnitlca, F. J. Prag Sb. (1893) (Mth.- 

Nt.) No. 47, 10 pp. 



[1843] 
141-, 
(1862) 78-, 

Mth. 2 (1863) 136-. 
Des Moines Anal. 4 (1877) 

Am. Ac. P. 13 (1878) 



Quaternions 0830 

Quaternions. Studnifka, F. J. Casopis 23 
(1894) 145-. 209- ; Fschr. Mth. (1893-94) 
135. 

and algebra of vectors. Gibbs, J. W. Nt. 
43 (1891) 511-. 

Am. Ph. S. P. ----- . Tait, P. G. Nt. 43 (1891) 608. 
----- . Gibbs, J. W. Nt. 47 (1892- 

93) 463-. 

----- . Gibbs, J. W. Nt. 48 (1893) 
364-. 

, application, new. Everett, J. D. B. A. 
Ep. (1874) (Sect.) 11. 

, applications to exponential and other 
functions. Studnicka, F. J. Prag Sb. 
(1894) (Mth.-Nt.) No. 7, 18 pp. 

, geometry of straight lines and 
complexes. Valentiner, H. Kitfb. Ov. (1899) 
655-. 

, -- mechanics. Sebuev, G. N. Kazan 
S. Ps.-Mth. Bll. 2 (1893) 111-; Fschr. Ps. 
(1893) (Ab. 1) 299. 

, and physics. Molenbroek, P. 
Amst. Ak. Vh. (Sect. 1) 2 (1894) No. 3, 
38 pp. ; Fschr. Mth. (1893-94) 1315-. 

, metrical geometry. Versluys, J. 
N. Arch. Wisk. 2 (*1876) 135-. 

, -- physics. Tait, P. G. QJ. Mth. 6 
(1864) 279-; Ph. Mg. 29 (1890) 84-. 

, --- . McAulay, A. [1892] Nt. 47 
(1892-93) 151. 

, projective geometry. Chapman, 
C. H. Am. J. Mth. 14 (1892) 115-. 

, study of quadrics. Papelier, . 
Par. S. Mth. Bll. 17 (1889) 182-. 

, -- theory of linear complex and linear 
congruence. Buchheim, A. Mess. Mth. 12 
(1883) 129-. 

, rotation. Cayley, A. Ph. 
Mg. 33 (1848) 196-. 

and "Ausdehnungslehre." Gibbs, J. W. 
Nt. 44 (1891) 79-. 

--- . Tait, P. G. Nt. 44 (1891) 105-. 

, -- , application to different kinds of 
uniform space. Cox, H. [1882] Camb. 
Ph. S. T. 13 (1883) 69-. 

, calculus, theorem, general. Graves, C. 
Ir. Ac. P. (1850) 347-. 

, Col. Hime's outlines of. Macfarlane, A. 
Ph. Mg. 39 (1895) 135-. 

, continued fractions in 

W. B. Ph. Mg. 3 (1852) 371- ; 4 
303; 5 (1853) 117-, 236-, 321-. 

, -- , and quadratic equations. Hamilton, 
(Sir) W. B. Ir. Ac. P. 5 (1853) 219-, 299-. 

, development of the A -process in. S)iaw, 
J. B. Am. J. Mth. 19 (1897) 193-. 

, elements. Bartlett, W. P. G. Camb. 
(M.) Mth. M. 2 (1860) 29-, 97-, 128-, 195-. 

, . Peddie, W. Edinb. Mth. S. P. 11 
(1893) 130-. 

, establishment of fundamental properties. 
McAulay, A. Mess. Mth. 18 (1889) 131-. 

, extensions. Hamilton, (Sir) W. B. Ph. 
Mg. 7 (1854) 492-; 8 (1854) 125-, 261- ; 
9 (1855) 46-, 280-. 

, and fourfold space. HatJiaway, A. S. 
[1897-1900] N. Y. Am. Mth. S. Bll. 4 
(1898) 54-; 7 (1901) 243, 245-. 

58 



Hamilton, (Sir) 
(1852) 



0830 Quaternions 

Quaternions, functions resembling. Cockle, 

Jas. Ph. Mg. 33 (1848) 435-. 
, Gauss' claim to invention. Tait, P. G. 

[1899] Edinb. B. S. P. 23 (1902) 17-. 
, general case of. Sylvester, J. J. C. B. 

99 (1884) 117-. 
, geometrical interpretation. Donkin, W. F. 

Ph. Mg. 36 (1850) 489-. 
_, . Spottiswoode, W. Ph. Mg. 37 

(1850) 108-. 
, geometry of. Paterson, J. Camb. and 

Dubl. Mth. J. 9 (1854) 241-. 
, theory. Hamilton, (Sir) W. E. 

Ir. Ac. P. 3 (1847) 31-. 
, involution and evolution. Sylvester, J. J. 

Ph. Mg. 16 (1883) 394-. 
, Klein's view. Knott, C. C. [1899] Edinb. 

B. S. P. 23 (1902) 24-. 
, and method of equipollences. Bellavitis, 

G. Yen. At. (1857-58) 334-; Mod. Mm. 

S. It. 1 (1862) 126-. 
, multinomial theorems. Wilkinson, (Eev.) 

M. M. U. [1890] Edinb. E. S. P. 17 

(1891) 149-. 
, multiplication, new proof of associative 

property. Versluys, J. [1871] Arch. Neerl. 

7 (1872) 177-. 
, nabla (V). Kimura, S. A. Mth. 10 

(1895-96) 127-. 
, nonions, sedenions, &c. Sylvester, J. J. 

(xn) [1883] J. H. Un. Cir. [3] (1884) 7-. 
, notes. Boole, G. (vi Adds.) Ph. Mg. 33 

(1848) 278-. 
, . Anthony, E. Mess. Mth. 10 (1881) 

66-. 

, . Kimura, S. Nt. 52 (1895) 366. 
, number-theory. Hurwitz, A. Gott. Nr. 

(1896) 313-. 

as a practical instrument of physical re- 
search. McAulay, A. Ph. Mg. 33 (1892) 

, principles elementarily explained. Padel- 

letti, D. G. Mt. 20 (1882) 1-. 
, , elementary, establishment on analytical 

basis. Plarr, G. [1874-77] Edinb. E. S. 

T. 27 (1876) 175- ; 28 (1879) 37-. 
, proof of Frobenius' theorem on their 

relation to complex numbers. Grissemann, 

F. X. Mh. Mth. Ps. 11 (1900) 132-. 
, property. Mounier, G. J. D. N. Arch. 

Wisk. 8 (*1882) 81-. 
, reduced form. Studnicka, F, J. Prag 

Sb. (1875) 183-. 
, relative forms. Peirce, C. S. (xn) J. H. 

Un. Cir. [1] (1882) 179. 
, and spherical geometry. MSbius, A. F. 

Leip. B. 11 (1859) 138-. 
, theory. Versluys, J. N. Arch. Wisk. 1 

(*1875) 41-, 97-; 2 (*1876) 135-. 
, . Sarran, E. A. Tel. 8 (1881) 52-, 

113-. 
, . Stephanos, C. Mth. A. 22 (1883) 

589-. 
, . Weyr, E. C. B. 98 (1884) 906-, 

1320-. 

, . Holder, 0. Gott. Nr. (1889) 34-. 
, . Study, E. N.-Vorp. Mt. 31 (1900) 1-. 



Ausdehnungslehre 0840 

Quaternions and vector analysis, principles. 

Peddie, W. Edinb. Mth. S. P. 11 (1893) 

85-. 
vectors. Knott, C. G. Nt. 48 

516-. 
Quotient of vectors in space, product of 

matrices. Wettum, T. B. van. N. Arch. 

Wisk. 1 (1895) 68-; Fschr. Mth. (1893- 

94) 226. 
Quotients of space-directed lines. Elliott, 

E. B. Smiths. Misc. Col. 33 (1888) Art. 4, 

106- ; (Wash. Ph. S. Bll. 10 (1888).) 
Surfaces, cubic, class treated by quaternions. 

Chace, A. B. Am. J. Mth. 2 (1879) 315-. 
, quadric, treated by quaternions. Lowell, 

A. L. Am. Ac. P. 13 (1878) 222-. 
, theorems. Hamilton, (Sir) W. E. Ir. 

Ac. P. 4 (1850) 306-. 
Symbolic cubic, particular case. Plarr, G. 

[1881] Edinb. B. S. P. 11 (1882) 342-. 

equation satisfied by symbol of operation 
on a quaternion, existence. Hamilton, 
(Sir) W. E. Ph. Mg. 24 (1862) 127-. 

integration of differential equations in 
quaternions. Pocklington, H. C. [1899] 
Camb. Ph. S. P. 10 (1900) 59-. 

Tait's elementary treatise, note on paragraphs 

439, 440. Plarr, G. C. E. 86 (1878) 1454-. 
Trigonometrical coefficients. Dierke, G. A. 

Educ. Times 41 (1888) 171. 
Trigonometry, plane, by quaternions. Wood, 

De V. Des Moines Anal. 9 (1882) 19-. 
Use of V - 1 and alternate numbers i, j, k in 

study of infinitesimal deformations. Perna, 

A. Palermo Cir. Mt. Ed. 12 (1898) 322-. 
Vector expressions for curves. Joly, C. J. 

Ir. Ac. P. 4 (1896-98) 374-. 
Vectorial equation of the circumference. 

Eaimondi, E. G. Mt. 25 (1887) 219-. 

function of 1st degree <f>p. Alberti, V. 
G. Mt. 37 (1899) 375-. 

Vectors and quaternions, theory. Beez, . 

Z. Mth. Ps. 41 (1896) 35-, 65-. 
Wave-surface, electromagnetic, quaternion 

treatment. Tait, P. G. [1894] Edinb. B. 

S. P. 21 (1897) 165-. 

, Fresnel's quaternion investigations. 
Tait, P. G. QJ. Mth. 3 (1860) 190-. 

0840 Ausdehnungslehre; vector 
analysis. 

Analytical geometry, use of imaginaries. 

Stille, W. A. Des Moines Anal. 1 [1874] 

181-. 
Area of any closed circuit in space. Hayward, 

E. B. L. Mth. S. P. 4 (1871-73) 289-. 
Associated poles, and their representation by 

products. Grassmann, H. Gott. Nr. (1872) 

567-. 
Ausdehnungen, multiple, simplest theorems. 

Hoppe, E. Arch. Mth. Ps. 64 (1879) 189-. 
"Ausdehnungslehre." Grassmann, H. Grunert 

Arch. 6 (1845) 337-. 
, geometric representation of imaginaries 

from standpoint of. Schlegel, S. F. V. 

Z. Mth. Ps. 23 (1878) 141-. 



59 



0840 



Ausdehnungslehre ; vector analysis 



"Ausdehnungslehre," Grassmann's. Schlegel, 
V. Z. Mth. Ps. 41 (1896) (H.-lt. Ab.) 1-, 

, , applications. Clifford, W. K. Am. 

J. Mth. 1 (1878) 350-. 
, , to mechanics. Schlegel, V. Giving. 

40 (1894) 59-. 
, , properties of circles. Cox, H. 

QJ. Mth. 25 (1891) 1-. 
, , relation to modern geometrical methods. 

Schlegel, S. F. V. Z. Mth. Ps. 24 (1879) 

83-. 
, mechanics according to principles of. 

Grassmann, H. G. Mth. A. 12 (1877) 222-. 
, and modern algebra. Grassmann, H. G. 

Mth. A. 7 (1874) 538-. 
, place in the associative algebra of quaternion 

type. Joly, C. J. Ir. Ac. P. 6 (1900-02) 

13-. 
Barycentre of curvature of plane curves. 

Steiner, J. G. Arcad. 101 (1844) 257-; 

102 (1845), 1-, 121-. 
Barycentric calculus, application to problems 

in analytical geometry. Minding, E. F. A. 

Crelle J. 5 (1829) 397-. 
based on composition of straight lines. 

Mdbius, A. F. Crelle J. 28 (1844) 1-. 
Complex function, construction, theorem of 

Picard. Stolz, O. [1880] Innsb. Nt. Md. 

B. 11 (1881) 27-. 

functions, geometric representation. 
Wittstein, T. Grunert Arch. 7 (1846) 411-. 

variables, extension to 3 dimension space. 
Hall, T. P. Iowa Ac. Sc. P. 6 (1899) 
202-. 

Composition of simultaneous and successive 
vectors. MacFarlane, A. Science 4 (1896) 
346. 

Crystallography, parameters of, and vectors 
of higher order. Voigt,W. Gott. Nr. (1900) 
355. 

Curves with branches in several planes, 
existence. (Geometrical interpretation of 
J - 1 and fractional powers). Gregory, 

D. F. Camb. Mth. J. 1 (1839) 259-. 
Directed magnitudes. Baiter, A. L. Rochester 

(N. Y.) Ac. Sc. P. 3 (1900) 162-. 
Directions and rotations, arithmetic. Berdelle, 

C. As. Fr. C. R. (1887) (Ft. 2) 197-. 
Directive algebra, application. Neuberg, J. 

(xn) Mathesis 1 (1881) 123-. 

, to geometry. Transon, A. N. A. 

Mth. 7 (1868) 145-, 193-, 241-. 

arithmetic. - Berdelle, C. As. Fr. C. R. 
(1888) (Pt. 2) 109-. 

Distance, theory. Clifford, W. K. B. A. Rp. 
39 (1869) (Sect.) 9. 

Diihring's vector conceptions. Wessely, K. 
Arch. Mth. Ps. 9 (1890) 393-. 

Electromagnetism, application of vector func- 
tions. Petrini, H. Ups. S. Sc. N. Acta 15 
(1895) No. 14, 60 pp. 

Equations in linear and vector functions, note 
on solution. Tait, P. G. Edinb. R. S. P. 
21 (1897) 497-. 

Equipollences, calculus, origin. Laquiere, 

E. M. As. Fr. C. R. (1881) 76-. 



0840 



Equipollences, graphic solution of geometrical 

problems. Bellavitis, G. [1842] Yen. Mm. 

I. 1 (1843) 225-. 
, method. Bellavitis, G. A. Sc. Lomb. 

Yen. 7 (1837) 243-; 8 (1838) 17-, 85-; 

Mod. Mm. S. It. 25 (1855) 225-. 

, origin. Bellavitis, G. Ven. I. Mm. 
19 (1876) 449-. 

, solution by. Bellavitis, G. G. Teix. 

J. Sc. 1 (1878) 145- ; 2 (1880) 3-. 

, proof of theorems by. Bellavitis, G. 
Ven. At. 6 (1847) 53-. 

, solution of a question. Monteiro, A. S. 
G. Teix. J. Sc. 2 (1880) 97-. 

External multiplication (i.e. use of alternate 
numbers) in algebra. Fehr, H. N. A. 
Mth. 14 (1895) 74-. 

Flat-space coordinates. Young, W. H. L. 
Mth. S. P. 30 (1899) 54-. 

Forces, composition, deduced from general 
principles. De Morgan, A. [1859] Camb. 
Ph. S. T. 10 (1864) 290-. 

Function of complex argument applied to 
lemniscate geometry, relationship, and kine- 
matics. Holzmiiller, F. G. Z. Mth. Ps. 
21 (1876) 325-. 

Functions of vectors, which are themselves vec- 
tors. Burkhardt, H. Gott. Nr. (1893) 155-. 

Geometric calculus, essay. Peano, G. Tor. 
Ac. Sc. At. 31 (1895) 552- or 952-. 

, principles. Macfarlane, A. [1900] N. 

Y. Am. Mth. S. Bll. 7 (1901) 158, 178. 

multiplication of surfaces. Chessin, A. S. 
A. Mth. 9 (1894-95) 70-. 

sums and differences. Barre de Saint- 
Venant, . C. R. 21 (1845) 620-. 

Geometry of arbitrary magnitudes. Bugaev, 
N. V. [1888] Rec. Mth. (Moscou) 14 
(1890) 394-; Fschr. Mth. (1891) 725-. 

Grassmann's geometrical theories. Ziicet, A. 
A. Mth. 2 (1885-86) 1-, 25-. 

method. Carvallo, E. N. A. Mth. 11 
(1892) 8-; 12 (1893) 454-. 

applied to prove theorems in deter- 
minants. Milller, E. Z. Mth. Ps. 44 
(1899) 28-. 

in projective geometry. Burali-Forti, 
C. Palermo Cir. Mt. Rd. 10 (1896) 177-, 
254-; 11 (1897) 64-. 

methods, applications. Mehmke, E. Z. 
Mth. Ps. 37 (1892) 305-. 

, [centroid of quadrilateral and 
pentagon]. Caspary, F. N. A. Mth. 17 
(1898) 389-. 

, to elementary mechanics. Genese, 

R. W. As. Fr. C. R. (1894) (Pt. 2) 211-. 

, quadric curves and surfaces. 
Miiller, E. Crelle J. Mth. 115 (1895) 234-. 

, vectors in a plane. Caspary, F. N. 
A. Mth. 18 (1899) 248-. 

numbers in intrinsic geometry. Cesaro, 
E. Rm. R. Ac. Line. Rd. 3 (1894) (Sem. 1) 
367-, 621. 

Hertz's and Poynting's equations. Donati, L. 

Bologna Ac. Sc. Mm. 7 (1897) 633-. 
Images in the representation of functions, 

theory. Harris, R. A. A. Mth. 4 (1888) 

65-, 128. 



60 



0840 



Ausdehnungslehre ; vector analysis 



0840 



Imaginary binary straight lines. Thieme, 

F. E. Arch. Mth. Ps. 59 (1876) 426-. 

geometry (higher). Bey el, C. Zur. Vjschr. 
31 (1886) 20-. 

of Lobatschewsky. Battaglini, G. Nap. 

Ed. 6 (1867) 157-. 
, applications of formulae. Suvorov, 

T. M. (xn) [1881] Kazan S. Nt. (Ps.- 

Mth.) P. 1 (1883) [No. 5] 4-. 

or lateral curves, main features of theory. 
Thieme, F. E. Arch. Mth. Ps. 58 (1876) 
185-. 

straight lines. Thieme, F. E. Arch. 

Mth. Ps. 58 (1876) 218-. 

values of a variable, geometric interpreta- 
tion. Moitchot, . C. B. 61 (1865) 113-. 

Line geometry on principles of ' ' Ausdehnungs- 

lehre." Miiller, E. Mh. Mth. Ps. 2 (1891) 

267-. 
Lineal multiplication of two factors. Collins, 

J. V. Am. As. P. (1899) 69-. 
Linear vector equation of central pedal of 

conic. Hart, H. [1882] Mess. Mth. 12 

(1883) 32-. 
equations, solution in special conditions. 

Elfrinkhof, L. van. N. Arch. Wisk. 19 

(1892) 132- ; Fschr. Mth. 24 (1895) 84. 

and vector function. Tait, P. G. Edinb. 
E. S. P. 21 (1897) 160-, 310- ; 22 (1900) 547-. 

vector functions, scalar invariants of two. 
Joly, C. J. [1895] Ir. Ac. T. 30 (1892-96) 
709-. 

, theory. Joly, C. J. [1894] Ir. Ac. 

Tr. 30 (1892-96) 587-. 
Lineo-linear vector functions. Hathaway, 

A. S. Am. As. P. (1892) 59-. 
Loci of the equations p = (f> w e and p = (p v \f/ v e. 

Hyde, E. W. Z. Mth. Ps. 42 (1897) 122-. 
Magnitudes possessing extension, measurement. 

Study, E. Wien Ak. Sb. 91 (1885) (Ab. 2) 

100-. 
Mixed products. Mueller, E. Mth. A. 48 

(1897) 589-. 
Moments of inertia (Grassmann's method). 

Mehmke, R. Mth. A. 23 (1884) 143-. 
Non-congruent quantities, geometrical division. 

Hyde, E. W. A. Mth. 4 (1888) 9-. 
Operations on imaginaries considered geometri- 
cally. Henkle, W. D. Des Moines Anal. 1 

(1874) 5-. 
Parallelogram of forces, analytical proof. 

Imschenetsky, W. G. Fschr. Ps. (1889) (Ab. 

1) 290-. 
Plane vectors, linear transformation. Peano, 

G. Tor. Ac. Sc. At. 31 (1895) 113- or 157-. 
Point pairs, and circles in space, treated by 

Grassmann's method. Miiller, E. Mh. 

Mth. Ps. 7 (1896) 77-. 
Polar affections of geometrical magnitudes 

in piano. (Direction of lines, etc.) 

" Lanivicensis," (Sylvester, J. J.). [18641 

Mess. Mth. 3 (1866) 11-. 
Polars, theory, and algebraic configurations, 

application of Ausdehnungslehre. Grass- 

mann, H. G. [1877] Crelle J. Mth. 84 

(1878) 273-. 
Quadruple algebra ; and equations of 5th order. 

Cockle, Jas. Ph. Mg. 35 (1849) 434-. 



Quaternions and " Ausdehnungslehre." Gibb, 

J. W. Nt. 44 (1891) 79-. 
. Tait, P. G. Nt. 44 (1891) 105-. 

complex variable theory, calculus 
including. Lipschitz, R. 0. S. C. B. 91 
(1880) 619-, 660-. 

, Hamilton's, place in Ausdehnungslehre. 
Grassmann, H. G. Mth. A. 12 (1877) 375-. 

and vector analysis. Gibbs, J. W. Nt. 48 
(1893) 364-. 

, principles. Peddie, W. Edinb. 

Mth. S. P. 11 (1893) 85-. 
vectors. Knott, C. G. Nt. 48 (1893) 

516-. 
Quotients of space directed lines. Elliott, E. B. 

Smiths. Misc. Col. 33 (1888) Art. 4, 106- ; 

(Wash. Ph. S. Bll. 10 (1888).) 
Beduction of vectors and metric properties. 

Andrade, J. C. B. 125 (1897) 394-. 
Bigid body, motion of (exercise in Grassmann's 

methods). Liiroth, J. Z. Mth. Ps. 43 (1898) 

243-. 
Botations. Burali Forti, C. Bll. Sc. Mth. 23 

(1899)82-. 
Screw as a unit in the Grassmannian system 

of the sixth order. Hyde, E. W. A. Mth. 8 

(1893-94) 38-. 
Self -con jugate linear and vector functions, 

property. Tait, P. G. [1871] Edinb. B. S. 

P. 7 (1872) 498-. 
Spherical geometry according to Grassmann. 

Miiller, E. Mh. Mth. Ps. 3 (1892) 365-; 

4 (1893) 1-, 93; 9 (1898) 269-. 
Symbolic forms. O'Brien, M. [1851] Phil. 

Trans. (1852) 161-. 
Symbolical geometry and mechanics. O'Brien, 

M. [1847] Camb. Ph. S. T. 8 (1849) 497-. 
Use of v 1 and alternate numbers i, j, k in 

study of infinitesimal deformations. Perna, 

A. Palermo Cir. Mt. Bd. 12 (1898) 322-. 
Vector analysis. Chapman, C. H. J. H. Un. 

Cir. [10 (1890-91)] 46-. 
. Tait, P. G. Nt. 47 (1892-93) 225-. 

. Donati, L. Bologna Ac. Sc. Mm. 7 

(1897) 11-. 

. Farkas, G. Mth. Termt. Ets. 16 

(1898) 321- ; Mth. Nt. B. Ung. 16 (1899) 
111-; Orv.-Termt. Ets. (Termt. Szak) (1899) 
91-; (1900) 1-, (Rv.)l-. 

. Burkliardt, H. D. Mth. Vr. Jbr. 5 

(1901) (Heft 1) 43-. 

, direct and logarithmic, &c. Malcor, 
(Capt.) . Bv. Mar. et Col. 76 (1883) 735-; 
77 (1883) 44-; 78 (1883) 416-. 

, a notation. Henrici, 0. B. A. Bp. 
(1897) 560-. 

, reality of roots of symbolical cubic. 
Tait, P. G. [1867] Edinb. B. S. P. 6 
(1869) 92-. 

conditions, integrability. Tait, P. G. 
[1877] Edinb. E. S. P. 9 (1878) 527-. 

, derivatives of a. Daniels, F. Z. Mth. Ps. 
45 (1900) 203-. 

differentiation. MacFarlane, A. [1900] 
Wash. Ph. S. Bll. 14 (1906) 73-. 

fields and fields of force. Broca, A. C. B. 
130 (1900) 109-. 



61 



0850 Matrices 

Vector fields, properties. Donati, L. Bologna 
Ac. Sc. Mm. 7 (1897) 427-. 

, theory, as preliminary to study of elec- 
tricity and magnetism. Ferraris, G. Tor. 
Ac. Sc. Mm. 47 (1897) 259-. 

functions. Burkhardt, H. Mth. A. 43 
(1893) 197-. 

quantities, certain. Bjerknes, V. Christiania 
Skr. (Mth.-Nt. Kl.) (1898) No. 4, 27pp. 

ratios considered as trigonometric functions 
of angles. Stringham, W. I. (xn) [1879] 
J. H. Un. Cir. [1] (1882) 35. 

Vectorial coordinates. Sylvester, J. J. Ph. 
Mg. 31 (1866) 287-, 380-. 

geometry on complexes of second order 
having a centre of figure. Genty, . 
Liouv. J. Mth. 8 (1882) 299-. 

Vectors, application to central motion. Cas- 
tellano, F. Tor. Ac. Sc. At. 29 (1894) 80-. 

, calculation with Ptolemy's theorem gene- 
ralised. Riecke,. Grunert Arch. 32 (1859) 
470-. 

of ellipse and related curves, sums and 
products. Schlomilch, 0. X. Z. Mth. Ps. 
26 (1881) 59-. 

, kinematic applications of theory. Cas- 
tellano, F. Ev. Mt. 2 (1892) 19-. 

and linear transformations, with physical 
applications. Carvallo, E. Mh. Mth. Ps. 
2 (1891) 177-, 225-, 311-. 

, , note on Carvallo's paper. 

Peano, G. Mh. Mth. Ps. 5 (1894) 136. 
quaternions. Knott, C. G. Nt. 48 (1893) 

148-. 
. Lodge, A. Nt. 48 (1893) 198-. 

. Macfarlane, A. Nt. 48 (1893) 
540-. 

, relation among four. Tail, P. G. [1889] 

Edinb. E. S. P. 16 (1890) 88-. 
, scalar relations connecting six. Wilkinson, 

(Rev.) M. M. U. [1889] Edinb. E. S. P. 16 

(1890) 773-. 
, theory. Zeiliger, D. N. N. Es. S. Nt. Mm. 

(Mth.) 11 (1890) 1-, 149- ; 13 [?1891] 1-; 

Fschr. Ps. (1890) (Ab. 1) 239. 
, , analysis. Peano, G. Tor. Ac. Sc. At. 

33 (1897) 313- or 513-. 
, recent innovations. Knott, C. G. 

[1892] Edinb. E. S. P. 19 (1893) 212-. 
, , teaching. Fontene, G. Ens. Mth 1 

(1899) 50-. 

versus quaternions. Heaviside, 0. Nt. 47 
(1892-93) 533-. 

Macfarlane, A. Nt. 48 (1893) 
75. 

which can be compounded, theory. 
Berruti, G. Tor. Ac. Sc. At. 29 (1894) 
115, 531-. 



0850 Matrices. 

Algebraic resolvents. Rados, G. Mth. Termt 



Birational transformations, prime factors 
Kantor, S. Mh. Mth. Ps. 10 (1899) 54-. 



Matrices 0850 

Characteristics of systems of three dimensions. 

Suvorov, T. M. (xn) Kazan Un. Mm. 7 

(1871) 3-. 
Complex numbers. Poincare, H. C. E. 99 

(1884) 740-. 
Differential equation to a curve of any order. 

Sylvester, J. J. Nt. 34 (1886) 365-. 
Elementary universal geometry, new terms. 

Sylvester, J. J. Nt. 32 (1885) 576-. 
Equations in matrices. Sylvester, J. J. J. H. 

Un. Cir. [3] (1884) 122. 
multiple quantity. Sylvester, J. J. Nt. 

31 (1885) 35-. 
Exchangeable matrices. Frobenius, G. Berl. 

Ak. Sb. (1896) 601-. 
Hamilton's quadratic equation, and the general 

unilateral equation in matrices. Sylvester, 

J. J. Ph. Mg. 18 (1884) 454-. 

a general method for unilateral 
equations in matrices of any order. Sylvester, 
J. J. C. E. 99 (1884) 621-. 

quaternions and Cayley's matrices. Wettum, 
T. B. van. N. Arch. Wisk. 17 (1890) 206- ; 
Fschr. Mth. (1890) 699-. 

Harriot's law on algebraic equations, extension 

to matrices. Sylvester, J. J. C. E. 98 

(1884) 1026-. 
Infinite and imaginary, use in service of finite 

and real. Sylvester, J. J. Nt. 32 (1885) 

103-, 271. ' 
Interpolation-formula in matrices, extension of 

Sylvester's. Buchheim, A. Ph. Mg. 22 (1886) 

173. 
Invariants, arithmetical, of a rectangular 

matrix. Smith, H. J. S. L. Mth. S. P 

4 (1871-73) 236-. 
Inverse orthogonal matrices, etc. Sylvester, 

J. J. Ph. Mg. 34 (1867) 461-. 
Involutant of two binary matrices. Cay ley, A. 

Mess. Mth. 20 (1891) 136-. 
Involutants and allied species of invariants to 

matrix systems. Sylvester, J. J. (xn) 

[1883-84] J. H. Un. Cir. [3] (1884) 9-, 

Involution of two matrices of second order. 

Sylvester, J. J. B. A. Ep. (1883) 430-. 
Linear equation in matrices of any order, 

general resolution. Sylvester, J. J. C. E. 

99 (1884) 409-, 432-, 481. 

trinomial equation in matrices of any 
order. Sylvester, J. J. C. E. 99 (1884) 
527-, 576. 

Matrical equation px = xq. Sylvester, J J 

C. E. 99 (1884) 67-, 115-. 
qQ-Qq' = 0. Cayley, A. Mess. Mth. 

14 (1885) 176-. 
00 = 00. Taber, H. Am. Ac. P. 26 

(1891) 64-. 
Matrices. Tyler, H. W. Erlang. Ps. Md. S 

Sb. 23 (1891) 33-. 
, application of theory to linear differential 

equations. Brill, J. Camb. Ph. S. P 8 

(1895) 201-. 

and associated systems of complex quan- 
tities. Weyr,E. Prag Sb. (1887) (Mth.-Nt.) 
616-. 

, classification. Weyr, E. C. E. 100 (1885) 
966. 



G2 



0850 Matrices 

Matrices, fundamental proposition. Weyr, E. 

Prag Sb. (1884) (Mth.-Nt.) 148- ; Fschr. 

Mth. (1885) 107. 
, multiplication of, identical relation. 

Kretowski, W. Krk. Ak. (Mt.-Prz.) Bz. 6 

(1893) 151- ; Fschr. Mth. (1893-94) 217. 
, note. Brill, J. [1895-97] L. Mth. S. P. 

27 (1896) 35-; 28 (1897) 368-. 
, product of two. Sardi, C. G. Mt. 5 (1867) 

, ' . Janni, V. G. Mt. 11 (1873) 

357-. 
, . Bonolis, A. G. Mt. 34 (1896) 

375-. 

and quaternions. Elfrinkhof, L. van. N. 
Arch. Wisk. 1 (1895) 88-; Fschr. Mth. 
(1893-94) 226-. 

satisfying a certain equation. Brunei, . 
Bordeaux S. Sc. Mm. 4 (1888) xxii. 

, spherical geometry theorem proved by. 
Chrystal, G. Edinb. Mth. S. P. 2 (1884) 45-. 

of substitution. Brunei, . Bordeaux 
S. Sc. Mm. 4 (1888) viii. 

, theorem by Cayley, proof. Forsyth, A. R. 

Mess. Mth. 13 (1884) 139-. 
, theory. Cayley, A. Phil. Trans. 148 

(1858) 17-; 156 (1866) 25-. 
, . Buchheim, A. L. Mth. S. P. 16 

(1884-85) 63-. 
, . Weyr, E. C. B. 100 (1885) 787-; 

Prag Sb. (1887) (Mth.-Nt.) 358-. 
, . Taber, H. Am. J. Mth. 12 (1890) 

337-. 
, , identities in. Taber, H. Am. J. Mth. 

13 (1891) 159-. 
Matrix, a. Ravut, L. N. A. Mth. 17 (1898) 

us-. 



(a, b) , . . ax + b 
. ', and function _, , 



Mess. Mth. 



(1880) 104-. 

of third order, square root of. Cayley, A. 
Edinb. B. S. P. 7 (1872) 675-. 

which represents a vector. Chapman, C. H. 
Am. J. Mth. 13 (1891) 363-. 

Monothetic equations. Sylvester, J. J. C. B. 

99 (1884) 13-. 
Non-degenerate matrices, Sylvester's theorem. 

Taber, H. Am. Ac. P. 27 (1893) 46-. 
Notation for matrices, etc. Cayley, A. Crelle 

J. 50 (1855) 277-. 
Quaternion equation qQ-Qq' = Q. Cayley, A. 

Mess. Mth. 14 (1885) 108-. 

matrix. Wettum, T. B. van. N. Arch. 
Wisk. 18 (1891) 168- ; Fschr. Mth. (1891) 

. Elfrinkhof, L. van. N. Arch. Wisk. 

19 (1892) 143- ; Fschr. Mth. (1892) 141-. 

symbols, application to matrix. Taber, H. 
[1890] L. Mth. S. P. 22 (1891) 67-. 

Boots of matrices. Metzler, W. H. Am. J. 

Mth. 14 (1892) 326-. 
unitary matrices. Sylvester, J. J. C. B. 

94 (1882) 396-. 
zeroidal matrices. Brunei, G. C. B. 

106 (1888) 467-. 
Split matrix, properties. Sylvester, J. J. (xn) 

J. H. Un. Cir. [1] (1882) 210-. 



Other Complex Numbers 0860 

Trinomial unilateral quadratic equation in 
matrices of second order. Sylvester, J. J. 
QJ. Mth. 20 (1885) 305-. 

Vectors and linear transformations, with physi- 
cal applications. Carvallo, E. Mh. Mth. 
Ps. 2 (1891) 177-, 225-, 311-. 

, , note on Carvallo's paper. 

Peano, G. Mh. Mth. Ps. 5 (1894) 136. 



0860 Other special sorts of 
complex numbers. 

Associative imaginaries. Cayley, A. (xn) J. 
H. Un. Cir. [1] (1882) 211-. 

Biquaternions. Clifford, W. K. L. Mth. S. 
P. 4 (1873) 381-. 

, application to plane geometry. Com- 
bebiac, . Par. S. Mth. Bll. 26 (1898) 
259-. 

, coplanar, or doubly complex quantities, 
theory. Seydler, A. J. Prag Sb. (1881) 80-. 

, geometrical interpretation of results. Ha- 
milton, (Sir) W. R. Ir. Ac. P. 5 T1853) 
388-. 

, memoir. Buchheim, A. Am. J. Mth. 7 
(1885) 293-. 

Classes of numbers derived from real numbers 
by dexter and sinister operations. Burali- 
Forti, C. Tor. Ac. Sc. At. 29 (1894) 382-. 

Complex functions, generalisation of founda- 
tions. Scheffers, G. Leip. Mth. Ps. B. 45, 
(1893) 828-; 46 (1894) 120-. 

numbers extended. Vahlen, T. Konigsb. 
Schr. 38 (1897) [72]-. 

formed from n principal units. Weier- 
strass, K. Gott. Nr. (1884) 395-. 

. Schwarz, H. A. Gott. 

Nr. (1884) 516-. 
. Dedekind, R. Gott. Nr. 

(1885) 141-. 

. Holder, 0. Gott. Nr. 

(1886) 241-. 

. Weyr, E. Bll. Sc. Mth. 

11 (1887) 205-. 
. Scheffers, G. Leip. 

Mth. Ps. B. 41 (1889) 290-. 
. Schur, F. Mth. A. 33 

(1889) 49-. 
. Gegenbauer, L. Mh. 

Mth. Ps. 2 (1891) 429-. 
. Hilbert, D. Gott. Nr. 

(1896) 179-. 

, general. Dedekind, R. Gott. Nr. 

(1887) 1-. 

and groups of transformations. Study, E. 

Leip. Mth. Ps. B. 41 (1889) 177. 
of n dimensions. Petersen, J. Gott. Nr. 

(1887) 489-. 
, real systems. Carton, E. C. B. 124 

(1897) 1296-. 

, systems. Study, E. Gott. Nr. (1889) 

237-. 
, . Carton, E. C. B. 124 (1897) 

1217-. 
, of higher. Molten, T. Mth. A. 41 

(1893) 83-; 42 (1893) 308-. 



63 



0870 Algebra of Logic 

Complex numbers, systems, reducibility. Schef- 

fers, G. Mth. A. 41 (1893) 601-. 
, , reduction to typical forms. Schef- 

fers, G. Mth. A. 39 (1891) 293-. 
, , theory. Hausdorff, F. Leip. Mth. 

Ps. B. 52 (1900) 43-. 
Elliptic and hyperbolic numbers. Levi-Civita, 

T. Ven. I. At. (1892-93) 1765-. 
Nonions analogous to quaternions, quantities 

forming a group. Sylvester, J. J. C. E. 97 

(1883) 1336- ; 98 (1884) 273-, 471-. 
, system. Peirce, C. S. (xn) J. H. Un. 

Cir. [2] (1883) 86-. 
, ( , represented by 9 matrices). Sylvester, 

J. J. (xn) J. H. Un. Cir. [1] (1882) 241- ; 

[2] (1883) 46, 86. 
Non-quaternion number-systems containing no 

skew units. Starkweather, G. P. Am. J. 

Mth. 21 (1899) 369-. 
Octonions. McAulay, A. B. S. P. 59 (1896) 

169-. 

Pluquaternions, and homoid products. Kirk- 
man, T. P. Ph. Mg. 33 (1848) 447-, 494-. 
Seven fundamental keys, system. Fontene, G. 

Par: S. Mth. Bll. 27 (1899) 171-. 
Symbolical and double numbers. Philippoff, M, 

Z. Mth. Ps. 37 (1892) 298-. 
Systems of numbers, calculation. Scheffers, G. 

Leip. Mth. Ps. B. 41 (1889) 400-. 

one-vectors in space of n dimensions. 
Young, W. H. L. Mth. S. P. 29 (1898) 
478-. 

Trinomial complex numbers. Schwering, K. 
Acta Mth. 10 (1887) 57-. 

Triquaternions. Combebiac, . Par. S. Mth. 
Bll. 27 (1899) 180-. 

Types of algebraical magnitudes arising by 
composition of two other types. Hensel, K. 
Crelle J. Mth. 105 (1889) 329-. 

Units of an w-fold space, applications. Chap- 
man. C. H. Am. J. Mth. 10 (1888) 225-. 

0870 Algebra of Logic. 

Abacus, logical. Jevons, W. S. Manch. Lt. 

Ph. S. P. 5 (1866) 161-. 
Algebra of binary relatives. Schroeder, E. 

Mth. A. 46 (1895) 144-.' 
logic. Peirce, C. S. Am. J. Mth. 3 

(1880) 15-. 
, a contribution to the philosophy of 

notation. Peirce, C. S. Am. J Mth 7 

(1885) 180-. 

, formulae. Peano, (?. Ev. Mt. 1 
(1891) 24-, 182-. 

, principles. Macfarlane, A. B. A. 

Ep. (1879) 262-. 
, . Peano, G. Ev. Mt. 1 (1891) 

, remark. Korselt, A. Mth. A. 44 

(1894} 156-. 
relations, principles. Schroder, F [1900] 

N. Y. Am. Mth. S. Bll. 7 (1901) 176-. 
Boole's analysis of logic. Harley, E. B. A. 

Ep. 36 (1866) (Sect.) 3-. 

laws of thought. Young, G. P. Cn J 10 
(1865) 161-. 



0870 Algebra of Logic 

Boole's laws of thought. Ellis, E. L. B. A. 

Ep. 40 (1870) (Sect.) 12-. 
. Harley, E. B. A. Ep. 40 (1870) 

(Sect.) 14-. 
Calculus of equivalent statements . Mac Coll,H. 

[1896-97] L. Mth. S. P. 28 (1897) 156-, 

555- ; 29 (1898) 98-. 
and integration limits. McColl, H. 

L. Mth. S. P. 9 (1877-78) 9-, 177- ; 10 

(1878-79) 16-; 11 (1879-80) 113-. 
logic. Boole, G. Camb. and Dubl. Mth. 

J. 3 (1848) 183-. 
. Cayley, A. QJ. Mth. 11 (1871) 

282-. 
, Boole's, improvement. Peirce, C. S. 

[1867] Am. Ac. P. 7 (1868) 250-. 
, cycle of operations of. Schroder, E. 

Mth. A. 12 (1877) 481-. 
, functional theorems. Nagy, A. Ev. 

Mt. 2 (1892) 177-. 
Deductive logic, principles. Vailati, G. Ev. 

Mt. 1 (1891) 127-. 
Dependence, property of, as a relation. Vailati, 

G. Ev. Mt. 2 (1892) 161-. 
Dialectics, rational. Gergonne, J. D. Gergonne 

A. Mth. 7 (1816-17) 189-. 
Elimination problem in identical calculus. 

Schroder, E. D. Nf. Tbl. (1885) 353-. 
Expressions for hypothetical and disjunctive 

propositions. Graves, C. Ir. Ac. P. 4 

(1850) 147-. 
Formal properties of algebraic operations. 

Burali-Forti, C. Ev. Mth. 6 (1896-99) 141-. 
Implicational and equational logic. McColl, H. 

[1880] Ph. Mg. 11 (1881) 40-. 
Inverse or inductive logical problem. Jevons, 

W. S. [1871] Manch. Lt. Ph. S. P. 11 

(1872) 65-. 
Jevons-Clifford problem. Nagy, A. Mh. Mth. 

Ps. 5 (1894) 331-. 
Law of roots in logic. Poretsky, P. Ev. Mth. 

6 (1896-99) 5-. 
Logic, algebraic analogues. Ellis, A. J. E. 

S. P. 21 (1873) 497-. 
, application to mathematics. Debrun, B. 

Niort. Mm. de l'Athene"e 1 (1808) 1-. 
, . Matzka, W. Grunert Arch. 6 

(1845) 353-. 
, formal. Ellis, A. J. E. S. P. 20 (1872) 

307-. 

of mathematics. Peirce, C. S. [1867] Am. 
Ac. P. 7 (1868) 402-. 

number. Peirce, C. S. Am. J. Mth. 4 

(1881) 85-. 
relatives, notation. Peirce, C. S. [1870] 

Am. Ac. Mm. 9 (pt. 2) (1873) 317-. 
, symbolic. MacColl, H. [1900] N. Y. Am. 

Mth. S. Bll. 7 (1901) 158, 166-. 
, treatment. Murphy, J. J. Manch. Lt. 

Ph. S. Mm. & P. 4 (1891) 201-. 
Logical calculus. Poreckij, P. S. Kazan S. 

Nt. (Ps.-Mth.) P. 7 (1889) 260-. 
. Nagy, A. G. Mt. 28 (1890) 1-. 

equalities, laws. Poreckij, P. S. Kazan 
S. Ps.-Mth. Bll. 8 (1899) 33-, 129-, 183- ; 
10 (1901) 50-, 132-, 191- ; 11 (1901) 17-. 

equations. Johnson, W. E. [1900] N. Y. 
Am. Mth. S. Bll. 7 (1901) 158, 177-. 



64 



0870 Algebra of Logic 

Logical equations, methods of solution, and 
inverse method of mathematical logic. 
Poryetskii, P. S. (xn) [1882] Kazan S. 
Nt. (Ps.-Mth.) P. 2 (1884) 161-. 

form of geometrical theorems. Macfarlane, 
A. A. Mth. 3 (1887) 154-. 

functions, theorems concerning. Nagy, A. 
Ev. Mth. 6 (1896-99) 21-. 

notation, a new system. Murphy, J. J. 
Manch. Lt. Ph. S. Mm. & P. 2 (1889) 
22-. 

propositions, on the transformations. 
Murphy, J. J. Manch. Lt. Ph. S. Mm. 8 

(1884) 132-. 

quantities, graphical representation. Nagy, 
A. Em. E. Ac. Line. Ed. 6 (1890) (Sem. 2) 
50-, 373-, 393. 

spectrum. Macfarlane, A. Ph. Mg. 19 

(1885) 286-. 

, method, application to Boole's pro- 
blem. Macfarlane, A. Am. As. P. (1890) 
57-. 

Magnitudes, theory. Burali-Forti, C. Ev. Mt. 

3 (1893) 76-. 

Mathematical logic, first principles. Poryetskii, 

P. S. (xn) [1880] Kazan S. Nt. (Ps.-Mth.) 

P. 1 (1883) [Ufa 2)] 2-. 
, some applications in arithmetic. B unite - 

kij, E. Fschr. Mth. (1897) 63. 
, studies. Peano, G. Tor. Ac. Sc. At. 

32 (1896) 361- or 565-. 
Mechanical performance of logical inference. 

Jevons, W. S. [1869] Phil. Trans. 160 

(1870) 497-. 
Notations, various, for expressing propositions 

of logic. Venn, J. [1880] Camb. Ph. S. P. 

4 (1883) 36-. 

Numerically definite propositions. Boole, G. 
[1868] Camb. Ph. S. T. 11 (pt. 2) (1869) 
396-. 

reasoning, system. Jevons, W. S. 
[1870] Manch. Lt. Ph. S. Mm. 4 (1871) 
330-. 

Eelation between the logical theory of classes 

and the geometrical theory of points. Kempe, 

A. B. [1890] L. Mth. S. P. 21 (1891) 

147-. 
Eelations between logical magnitudes. Nagy, A . 

Mh. Mth. Ps. 4 (1893) 147-. 
members of a system. Amicis, E. de. 

Ev. Mt. 2 (1892) 113-. 
Straight lines, fundamental geometry of. 

Vaikiti, G. Ev. Mt. 2 (1892) 71-. 
Syllogism, on the. Harris, J. R. J. H. Un. 

Cir. [3] (1884) 130-. 

Syllogisms of transposed quantity. De Mor- 
gan, A. Camb. Ph. S. T. 10 (1864) 

355*-. 
Symbolical language, growth and use. McColl, 

H. [1881] Manch. Lt. Ph. S. Mm. 7 (1882) 

225-. 
Symbols of logic, and theory of the syllogism. 

De Morgan, A. [1846-50] Camb. Ph. S. T. 

8 (1849) 379- ; 9 (1856) 79-. 
Types of compound statement involving 4 

classes. Clifford, W. K. Manch. Lt. Ph. 

S. P. 16 (1877) 88-. 

VOL. I. 



Theory of Groups. General 1200 

Theory of Groups. 
1200 General 

Adjoint operations. Pincherle, S. Bologna Ed. 

2 (1898) 130-. 
Anharmonic curves. Bioche, C. Par. S. Phlm. 

Bll. 5 (1893) (C. R. No. 10) 2. 
Constancy of factor-groups, Holder's theorem. 

Brown, G. L. N. Y. Am. Mth. S. Bll. 1 

(1895) 232-. 

Distributive operations and homography. Pin- 
cherle, S. Mil. I. Lomb. Ed. 29 (1896) 397-. 
Finite and infinite groups. Bettazzi, R. Tor. 

Ac. Sc. At. 31 (1895) 362- or 506-. 
Functional substitution equations. Bottcher, E. 

Wiad. Mt. 4 (1900) 233-. 
Group-characteristics. Frobenius, G. Berl. 

Ak. Sb. (1896) 985-. 
, composition. Frobenius, G. Berl. Ak. 

Sb. (1899) 330-. 
and subgroups, relations. Frobenius, G. 

Berl. Ak. Sb. (1898) 501-. 
Group and number. Bettazzi, R. Tor. Ac. 

Sc. At. 31 (1895) 304- or 446-. 

theory and its application. Zorawski, K. 
Krk. Ak. (Mt.-Prz.) Ez. 6 (1893) 289-; Crc. 
Ac. Sc. Bll. (1893) 145-. 

Groups, complete theory. Kirkman, T. P. 
[1863] Manch. Ph. S. P. 3 (1862-63) 133-, 
161- ; 4 (1865) 171-. 

depending on n =l. Cayley, A. Ph. Mg. 
7 (1854) 40-, 408 ; 18 (1859) 34-. 

of functions. Pincherle, S. Bologna Ac. 
Sc. Mm. 6 (1884) 205-. 

, functions given by. Kirkman, T. P. 
Manch. Lt. Ph. S. Mm. & P. 4 (1891) 315- ; 
5 (1892) 23-. 

and generators, systems. Fulco, P. Catania 
Ac. Gioen. At. 12 (1899) Mm. 12, 14 pp. 

of interchangeable elements. Frobenius, G. , 
<& Stickelberger, L. [1878] Crelle J. Mth. 
86 (1879) 217-. 

involution, transformations. Montesano, 

D. Yen. I. At. (1887-88) 1425-. 

and many -valued functions. Kirkman, T. P. 
[1861] Manch. Ph. S. Mm. 1 (1862) 274-. 

of order 8 !/2. Schottenfels, I. M. N. Y. 
Am. Mth. S. Bll. 6 (1900) 440-. 

related to regular bodies in n -dimensional 
space. Schoute, P. H. B. A. Ep. (1894) 
562-. 

, systems of. Dickson, L. E. N. Y. Am. 

Mth. S. Bll. 3 (1897) 265-. 
, theory. Cayley, A. [1877-89] L. Mth. 

S. P. 9 (1877-78) 126- ; Am. J. Mth. 11 

(1889) 139-. 
, and graphical representation. Cayley, A. 

Am. J. Mth. 1 (1878) 174- . 
Imprimitive groups. Kuhn, H. W. N. Y Am 

Mth. S. Bll. 7 (1901) 113, 116-. 

and soluble groups. Soderberg, J. T. [1899] 
Ups. S. Sc. N. Acta 20 (1904) No. 1, 26 pp. 

Infinite order, groups of. Miller, G. A. [1900] 
N. Y. Am. Mth. S. Bll. 7 (1901) 121-. 



65 



1200 Theory of Groups. General 

Invariants of groups of linear substitutions. 
Molien, T. Berl. Ak. Sb. (1897) 1152-. 

Inversion groups on quadric surfaces. Kasner, 
E. N. Y. Am. Mth. S. T. 1 (1900) 430-. 

Linear differential equations, arithmetical de- 
velopments. Fricke, R. D. Mth. Vr. Jbr. 
2 (1893) 59-. 

, form of integrals. Johanson, A. M. 

Stockh. Ofv. (1889) 583-. 

, theory. Volterra, V. Em. S. It. 

Mm. 6 (1887) No. 8, 104 pp. 

groups of functions. Pincherle, S. Bologna 
Ac. Sc. Mm. 6 (1884) 101-. 

, report on recent progress. Dickson, L. E. 

[1899] N. Y. Am. Mth. S. Bll. 6 (1900) 

13-. 
Maximum groups. Kirkman, T. P. Manch. 

Ph. S. P. 3 (1862-63) 59-. 
Non-isomorphic simple groups of the same 

order. Schottenfels, I. M. [1898] A. Mth. 

1 (1900) 147-. 

-modular groups. Kirkman, T. P. (m) 
[1862] Manch. Ph. S. Mm. 2 (1865) 204-. 

Popular account of new fields of mathematics. 

Miller, G. A. Science 11 (1900) 528-. 
Prime factors of the group-determinant. Fro- 
benius, G. Berl. Ak. Sb. (1896) 1343-. 
Eational and linear substitutions, the group of. 

Cordone, G. Tor. Ac. Sc. At. 31 (1895) 472- 

or 804- . 
Eegions of discontinuity for groups of real 

linear substitutions of a complex variable. 

Fricke, R. Gott. Nr. (1895) 360-. 
Eepresentation of finite groups by linear sub- 
stitutions. Frobenius, G. Berl. Ak. Sb. 

(1897) 995-; (1899) 482-. 
Euled surfaces admitting homographic auto- 
morphic transformation. Bioche, C. Par. 

S. Phlm. Bll. 4 (1892) 130-. 
Singular transformations of groups. Taber, H. 

N. Y. Am. Mth. S. Bll. 6 (1900) 199-. 
. Newson, H. B. N. Y. Am. Mth. 

S. Bll. 6 (1900) 431-. 
Sub-groups of doubly infinite series of simple 

groups. Wiman, A. Stockh. Ak. Hndl. 

Bh. 25 (1900) (Afd. 1) No. 2, 47 pp. 
general projective group. Taber, H. 

N. Y. Am. Mth. S. Bll. 2 (1896) 221-, 

346. 
Substitution groups, fundamental theorem. 

Miller, G. A. [1895] N. Y. Am. Mth. S. 

Bll. 2 (1896) 75-. 
Substitutions. Zochios, . C. E. 120 (1895) 

766-. 
Symmetrical group, characteristics. Frobenius, 

G. Berl. Ak. Sb. (1900) 516-. 
Test of a simple group. Miller, G. A. N. Y. 

Am. Mth. S. Bll. 1 (1895) 124-. 
Uniform substitutions. Koenigs, G. Bll. Sc. 

Mth. As. 7 (1883) 340-. 

. Podetti, F. G. Mt. 35 (1897) 264-. 

Vanishing groups. Cockle, Jas. Camb. and 

Dubl. Mth. J. 6 (1851) 174- ; 7 (1852) 114- ; 

8 (1853) 50-. 



Discrete Groups 1210 

1210 Discrete groups of finite and 
of infinite order (including 
groups of permutations). See 
also 2450, 4440. 

Abelian general linear group, new definition. 
Dickson, L. E. N. Y. Am. Mth. S. T. 1 
(1900) 91-. 

groups. Heffter, L. Crelle J. Mth. 119 
(1898) 261-. 

. Searpu, U. G. Mt. 38 (1900) 225-. 

and linear modular systems. Fund, 0. 
Hamb. Mth. Gs. Mt. 3 (1900) 371-. 

, and their application to number theory. 

Zsigmondy, K. Mh. Mth. Ps. 7 (1896) 

185-. 
Abstract group isomorphic with the symmetric 

group on k letters. Dickson, L. E. L. Mth. 

S. P. 31 (1900) 351-. 

groups of degree 32. Bagnera, G. A. Mt. 
2 (1899) 263-. 

order *1 and J*!. Moore, E. H. 

[1896] L. Mth. S. P. 28 (1897) 357-. 

simple group of order 2 7 . 3 6 . 5 . 7, a certain. 
Dickson, L. E. N. Y. Am. Mth. S. T. 1 
(1900) 353-, 509. 

Alternating group, uniform character. Beke, E. 
Mth. A. 49 (1897) 581-. 

groups. Kbnig, G. (xii) Mth. Tennt. Ets. 
1 (1883) 213- ; Mth. Nt. B. Ung. 1 (1882-83) 
191-. 

Analytical representation of a heptagram. 
Rogers, L. J. [1890] L. Mth. S. P. 22 
(1891) 37-. 

Arithmetical group, laws of reciprocity and sub- 
groups. Stouff, X. Par. 6c. Norm. A. 10 
(1893) 295-. 

Automorphic functions of two variables. Pi- 
card, E. Acta Mth. 1 (1882) 297- ; C. B. 
97 (1883) 1045-. 

modular groups. Fricke, R. Gott. Nr. 
(1896) 91-. 

Binary forms with linear automorphic trans- 
formations. Klein, C. F. [1875] Mth. A. 
9 (1876) 183-. 

Cayley's color-diagrams, representations of 
finite groups. Maschke, H. Am. J. Mth. 
18 (1896) 156-. 

Characteristics of types 3 & 4 and their sub- 
stitution groups. Pascal, E. A. Mt. 20 
(1892-93) 163- ; Bm. E. Ac. Line. Ed. 2 
(1893) (Sem. 1) 120-. 

Commutator groups. Miller, G. A. N. Y. 
Am. Mth. S. Bll. 4 (1898) 135-. 

Commutators of given group. Miller, G. A. 
[1899] N. Y. Am. Mth. S. Bll. 6 (1900) 105-. 

Composite groups. Bumside, W. Mess. Mth. 
24 (1895) 82-. 

, formation. Holder, O. Mth. A. 46 
(1895) 321-. 

, theory. Netto, E. Crelle J. Mth. 78 

(1874) 81-. 
Configuration of 140 straight lines in space. 

Maschke, H. Mth. A. 36 (1890) 190-. 



66 



1210 



Discrete Groups of Finite and of Infinite Order 



1210 



Congruence-group contained in the group of 
linear fractional substitutions. Moore, E. H. 
Am. As. P. (1892) 62. 

groups of prime rank. Gierster, J. Mth. 
A. 22 (1883) 111-. 

, theorem. Brioschi, F. Mil. I. Lomb. 

Ed. 12 (1879) 483-. 

Congruences, class of groups denned by. Burn- 
side, W. L. Mth. S. P. 25 (1894) 113- ; 26 

(1895) 58-. 

Conjugate system of linear substitutions, for- 
mation. Baraniecki, M. A. Par. T. Nauk 
Sc. Pam. 10 (*1878) Art. 3, 8 pp. 

Connexion in series and theory of substitutions. 
Hoyer, P. Mth. A. 42 (1893) 58- ; 49 (1897) 
39-. 

Crystalline structure and regular point groups. 
Rohn, K. Leip. Mth. Ps. B. 51 (1899) 
(Mth.) 445-. 

Cubic surfaces with automorphic collineations. 
Bobek, K. Mh. Mth. Ps. 10 (1899) 122-, 
307-. 

, polar hexahedra. Cremona, L. D. Nf. 

B. (*1877) 93-. 

Cyclic subgroups of simple ternary linear 
fractional group in a Galois field. Dickson, 
L. E. Am. J. Mth. 22 (1900) 231-. 

Direct product groups. Miller, G. A. N. Y. 
Am. Mth. S. T. 1 (1900) 66-. 

Discontinuity in certain homographies. Fricke, 
E. Mth. A. 47 (1896) 557-. 

Discontinuous groups. Poincare, H. C. E. 

94 (1882) 840-. 

in biquadratic field. Fricke, R. Gott. 

Nr. (1892) 268-. 
and quadratic forms. Picard, E. C. E. 

95 (1882) 763-. 

of real linear substitutions (Poincare's). 

Kepinski, S. Krk. Ak. (Mt.-Prz.) Ez. 6 
(1893) 37- ; Fschr. Mth. (1893-94) 207-. 

Doubly transitive groups of degree n and order 
n(n-l). Burnside, W. Mess. Mth. 25 

(1896) 147-. 

2 TO and order 2 (2 m - 1) . Burn- 
side, W. Mess. Mth. 25 (1896) 187-. 

substitutions of three degrees. 
Maillet, E. Par. S. Mth. Bll. 25 (1897) 
189-. 

Exchangeable and decomposable groups. 
Maillet, E. Par. S. Mth. Bll. 28 (1900) 

Finite group, definition. Bettazzi, R. Tor. 
Ac. Sc. At. 32 (1896) 240 or 352-. 

groups. Frobenius, G. Berl. Ak. Sb. (1895) 
163-. 

. Maillet, E. QJ. Mth. 29 (1898) 
250-. 

. Bauer, M. Mth. Tennt. fits. 17 
(1899) 611- ; N. A. Mth. 19 (1900) 508-. 

, class of. Burnside, W. Camb. Ph. S. 

T. 18 (1900) 269-. 

contained in group of quadratic homo- 
geneous transformations. Autonne, L. C. E. 
97 (1883) 567-. 

linear group, determination. 
Jordan, C. Nap. Ac. At. 8 (1879) No. 11 
41 pp. 



Finite groups contained in linear groups, class. 
Jordan, C. Par. S. Mth. Bll. 5 (1877) 175-. 

of correlations. Kantor, S. Crelle J. 
Mth. 116 (1896) 171-. 

whose degree is the fifth power of a 

prime. Bagnera, G. A. Mt. 1 (1898) 137-. 

of linear substitutions, fundamental pro- 
position in theory. Burkhardt, H. Mth. A. 
41 (1893) 309-. 

, theorem on. Klein, F. D. 

Nf. Vh. (1896) (Th. 2, Hdlfte 1) 5 ; D. Mth. 
Vr. Jbr. 5 (1901) (Heft 1) 57. 

transformations of a variable. 
Gordan, P. Mth. A. 12 (1877) 23-. 

. Cayley, A. [1879] 

Mth. A. 16 (1880) 260-, 439-. 
. Fano, G. Mh. Mth. 

Ps. 7 (1896) 297-. 
, report on. Miller, G. A. [1898] N. Y. 

Am. Mth. S. Bll. 5 (1899) 227-. 
-, sets of operations in relation to. White- 
head, A. N. E. S. P. 64 (1899) 319-. 
, theory. Valentiner, H. Kjtfb. Dn. Vd. 

Selsk. Skr. 5 (1889-91) 63- (with French 

resume). 
, . Burnside, W. [1893-95] L. Mth. 

S. P. 25 (1894) 9-; 26 (1895) 191-, 325-, 

559. 

, . Bauer, M. N. A. Mth. 19 (1900) 59-. 

Functions, cyclic. Dziobek, O. Arch. Mth. 

Ps. 69 (1883) 265-. 
, linear rational, taken according to prime 

modulus, and substitutions to which they 

lead. Serret, J. A. C. E. 48 (1859) 112-, 

178-, 237-. 
, , of several variables, values. Capelli, A. 

G. Mt. 14 (1876) 141-. 
, number of values, by permutations of 

letters. Bertrand, J. Par. 6c. Pol. J. 

30 8 cah. (1845) 123-. 
, , (Bertrand). Serret, 

J. A. Liouv. J. Mth. 14 (1849) 135-. 
, , . Despeyrons, C. 

Liouv. J. Mth. 10 (1865) 55-. 
, polynomial, admitting of reduction in 

number of variables. Sylvester, J. J. Ph. 

Mg. 5 (1853) 119-. 

proper to represent substitution of prime 
number of letters. Rogers, L. J. Mess. 
Mth. 21 (1892) 44-. 

reproduced by substitution. Cauchy, A. L. 
C. E. 19 (1844) 1436-. 

of several quantities, nature, formation, 
and substitutions rendering invariable. 
Mathieu, E. Liouv. J. Mth. 6 (1861) 241- ; 
N. A. Mth. 1 (1862) 227-. 

5 or 6 letters, especially those doubly 
"transitive. Cauchy, A. L. C. E. 21 (1845) 

1401- ; 22 (1846) 1-. 
4, 5, or 6 letters. Serret, J. A. Liouv. 

J. Mth. 15 (1850) 45-. 
6 letters, unsymmetrical, historical origin. 

Sylvester, J. J. Ph. Mg. 21 (1861) 369-. 
7 letters. Hermite, C. C. E. 57 (1863) 

750-. 
. Brioschi, F. C. E. 95 (1882) 

665-, 814-, 1254-. 



67 



1210 



Discrete Groups of Finite and of Infinite Order 



1210 



Galoisian groups. Perott, J. Par. S. Mth. 

Bll. 21 (1893) 61-. 
Generators of a symmetric group. Capelli, A . 

Q. Mt. 35 (1897) 354-. 
Geometrical operations, certain. Fleuri, G. 

N. S. W. E. S. J. 26 (1892) 60-. 
Group belonging to irreducible equations of 

prime degree. Sylow, L. [1867] Christiania 

F. 10 (1868) 105-. 

of discrete operations, definition. Dyck, W. 
[1881-82] Mth. A. 20 (1882) 1- ; 22 (1883) 
70-. 

modular equations. Gierster, J. Leip. 

Mth. Ps. B. 37 (1885) 291- ; Mth. A. 26 
(1886) 309-. 

theory. Guccia, G. B. Palermo Cir. Mt. 
Ed. 1 (1887) 388-. 

and algebraic equations. Foglini, G. 

Em. N. Line. Mm. 3 (1888) 3-; 7 (1891) 

175-. 
. Bolza, 0. Am. J. Mth. 13 

(1891) 59-. 
. Soderberg, J. T. Ups. S. Sc. 

N. Acta 15 (1895) No, 2, 38 pp. 
, geometrical treatment. Paolis, E. de. 

Em. S. It. Mm. 7 (1890) No. 6, 164 pp. 

, investigations. Frobenius, G. Crelle 
J. Mth. 101 (1887) 273-. 

and regular solids. Schoute, P. H. 
N. Arch. Wisk. 20 (1893) 100-. 

of 360 collineations in plane. Fricke, E. 
D. Nf. Vh. (1896) (Th. 2, Halfte 1) 5. 

Groups, Burnside's theory. Miller, G. A. 
N. Y. Am. Mth. S. Bll. 5 (1899) 249-. 

which can be represented as multiply transi- 
tive substitution groups. Miller, G. A. Mess. 
Mth. 28 (1899) 104-. 

of class n - u, degree n, at least u - 1 times 
transitive. Maillet, E. Par. 6c. Pol. J. 5 
(1900) 47-. 

degree p and order p(p + l)ir, p being 

prime, ir a divisor of p-1. Sylow, L. 

Christiania Skr. (Mth. Nt. Kl.) (1897) No. 9, 

19pp. 
, especially substitutions permutable with 

given one. Capelli, A. G. Mt. 14 (1876) 66-. 

formed of a finite number of linear substitu- 
tions. Jordan, C. C. E. 83 (1876) 1035- ; 
84 (1877) 1446-. 

of linear substitutions. Bianchi, L. Mth. 
A. 42 (1893) 30-. 

with coefficients belonging to 
imaginary quadratic corpora. Bianchi, L. 
Mth. A. 40 (1892) 332-. 

complex coefficients, some 
classes of. Bianchi, L. Mth. A. 43 (1893) 
101-. 

integral complex coefficients 

with applications to theory of numbers. 
Bianchi, L. Em. E. Ac. Line. Ed. 6 (1890) 
(Sent. 1) 331- ; Mth. A. 38 (1891) 313-. 

, theory. Loewy, A. Mth. A. 53 

(1900) 225-. 

, list of systems. Dickson, L. E. NY Am 
Mth. S. Bll. 5 (1899) 470-. 

of n dimensions. Frattini, G. Em. E. Ac. 
Line. T. 8 (1884) 260-. 



Groups of numbers in algebraic corpora. 
Weber, H. Mth. A. 48 (1897) 433-; 49 
(1897) 83-; 50 (1898) 1-. 

whose order is a number without square 
factors. Holder, O. Gott. Nr. (1895) 211-. 

power of prime, determination. 

Young, J. W. A. Am. J. Mth. 15 (1893) 
124-. 

, theory. Bauer, M. 

Mth. Termt. fits. 18 (1900) 133-. 

of order p m q i . Jordan, C. Liouv. J. Mth. 
4 (1898) 21-. 

p^q 2 , p and q being primes. Le Va- 

vasseur, E. P. C. E. 128 (1899) 1152-. 

16p, p being an odd prime. Le Va- 

vasseur, E. P. C. E. 129 (1899) 26-. 

P 3 q. Western, A. E. L. Mth. S. P. 

30 (1899) 209-. 

whose orders are products of three prime 
factors. Cole, E. N., & Glover, J. W. Am. 
J. Mth. 15 (1893) 191-. 

of orders p 3 , pq z , pqr, p*. Holder, 0. Mth. 
A. 43 (1893) 301-. 

which r arbitrary points in space of n di- 
mensions can represent. Schlegel, V. Arch. 
Mth. Ps. 10 (1891) 283-. 

several times transitive, elementary proper- 
ties. Cesaro, E. G. Mt. 22 (1884) 47-. 

and substitutions, new basis for theory. 
Hoyer, P. Mth. A. 51 (1899) 445-. 

, theorem. Cayley, A. Mth. A. 13 (1878) 

561-. 
, theorems. Kirkman, T. P. Manch. Ph. 

S. P. 2 (1860-62) 73-. 
, theory. Burnside, W. Mess. Mth. 23 

(1894) 50-; 24 (1895) 191-. 
Holoedric transformation into itself of a given 

group. Moore, E. H. [1895] N. Y. Am. 

Mth. S. Bll. 1 (1895) 61-; 2 (1896) 33-. 

and transitive isomorphs of symmetric or 
alternant groups. Maillet, E. Liouv. J. 
Mth. 1 (1895) 5-. 

Holomorph of the cyclical group, and some 
subgroups. Miller, G. A. QJ. Mth. 31 
(1900) 382-. 

Homogeneous substitution groups, theory. 
Molien, T. Dorpat Sb. 11 (1896) 259-. 

Hyperabelian groups, special class. Bourget, H. 
Toul. Fac. Sc. A. 12 (1898) D, 90 pp. 

Hyperelliptic curves of class 3, allowing auto- 
morphic transformation. Wiman, A. [1895] 
Stockh. Ak. Hndl. Bh. 21 (Afd. 1) (1896) 
No. 1, 23 pp. 

Hypergeometric functions with the branch 
points (2, 3, 7), (2, 4, 7), arithmetical theory. 
Fricke, E. Mth. A. 41 (1893) 443-. 

Hypoabelian group, first, generalised. Dick- 
son, L. E. QJ. Mth. 30 (1899) 1-. 

groups. Dickson, L. E. N. Y. Am. Mth. 
S. Bll. 4 (1898) 495-. 

Icosahedral group, construction. Bagnera, G. 
Palermo Cir. Mt. Ed. 11 (1897) 87-. 

substitutions, the sixty. Cayley, A. QJ. 
Mth. 27 (1895) 236-. 

Imprimitive and soluble groups. Soderberg, 
J. T. Ups. S. Sc. N. Acta 20 (1904) No. 1, 
26pp. 



1210 



Discrete Groups of Finite and of Infinite Order 



1210 



Imprimitive substitution groups of degree ten. 

Miller, G. A. N. Y. Am. Mth. S. Bll. 1 

(1895) 67-. 
Induced linear substitutions, groups. Rados, G. 

Mth. Termt. Ets. 17 (1899) 44-; Mth. Nt. 

B. Ung. 17 (1901) 227-. 
Intransitive groups, construction. Bolza, 0. 

Am. J. Mth. 11 (1889) 195-. 

linear substitution-groups. Maschke, H. 
Mth. A. 52 (1899) 363-. 

substitution groups of ten letters. Miller, 
G. A. QJ. Mth. 27 (1895) 99-. 

Invariance of factors of a substitution-group. 
Pierpont, J. Am. J. Mth. 18 (1896) 153-. 

Invariant expression for Poincare's substitu- 
tions. Brun, F. de. Stockh. Ofv. (1890) 
265-; Fschr. Mth. (1890) 410. 

Invariants attached to Klein's group 168. 
Boulanger, A. C. E. 130 (1900) 107-. 

of a quadrangle by protective transformation. 
Lovett, E. 0. A. Mth. 12 (1898-99) 79-. 

relative to the Hessian group. Boulanger, 
. C. E. 122 (1896) 178-. 

of substitutions of a Kleinian group. 
Bagnera, G. Em. E. Ac. Line. Ed. 7 
(1898) (Sem. 1) 340-. 

of ternary monomial groups. Skinner, 
E. B. [1900] N. Y. Am. Mth. S. Bll. 7 
(1901) 244, 256. 

Isomorphism, double, in group theory. 
Frattini, G. Em. E. Ac. Line. Ed. 2 

(1893) (Sem. 1) 253-. 

of a group with itself. Burnside, W. L. 
Mth. S. P. 27 (1896) 354-. 

of groups of substitutions. Capelli, A . G. 
Mt. 16 (1878) 32-. 

of simple linear groups. Dickson, L. E. 
N. Y. Am. Mth. S. Bll. 6 (1900) 323-. 

Isomorphisms, group of. Miller, G. A. N. 

Y. Am. Mth. S. Bll. 6 (1900) 337-. 
, groups of. Miller, G. A. C. E. 130 

(1900) 316-. 
, with same groups of. Miller, G. A. 

N. Y. Am. Mth. S. T. 1 (1900) 395-. 

of (Gp)*, p a prime greater than 3, study of. 
Le Vavasseur, R. P. Par. EC. Norm. A. 
16 (1899) 377-. 

a Hamiltonian group to itself, the 
simple. Miller, G. A. N. Y. Am. Mth. S. 
Bll. 5 (1899) 292-. 

substitution group to itself, the 
simple. Miller, G. A. Ph. Mg. 45 (1898) 
234-. 

Kirkman's problem, application of theory of 
groups to. Burnside, W. Mess. Mth. 23 

(1894) 137-. 

Kleinian groups. Poincarg, H. C. E. 93 
(1881) 44-; Acta Mth. 3 (1883) 49-. 

with two variables. Pezzo, P. del. 
Nap. Ed. 32 (1893) 123-. 

Klein's group of ( + !)! 7i-ary collineations. 

Moore, E. H. Am. J. Mth. 22 (1900) 336-. 
Kummer surface, birational transformations of. 

Hutchinson, J. I. [1900] N. Y. Am. Mth. 

S. Bll. 7 (1901) 211-. 
Lagrange and theory of groups. Pierpont, J. 

N. Y. Am. Mth. S. Bll. 1 (1895) 196-. 



Limit of transitivity of non-alternate groups. 

Jordan, C. (x) Par. S. Mth. Bll. 1 (1873) 

40-; Liouv. J. Mth. 1 (1895) 35-. 
. Miller, G. A. N. Y. 

Am. Mth. S. Bll. 4 (1898) 140-. 
substitution-groups. Bochert, A. 

Mth. A. 29 (1887) 27-; 33 (1889) 572-; 40 

(1892) 176-. 
Linear differential equations with algebraic 

integrals. Jordan, C. [1877] Crelle J. Mth. 

84 (1878) 89-. 

group of Borchardt's moduli. Maschke, 
H. Gott. Nr. (1887) 421- ; Mth. A. 30 
(1887) 496. 

groups of finite order with three variables. 
Picard, E. Par. S. Mth. Bll. 15 (1887) 152-. 

including the Abelian group. Dickson, 

L. E. QJ. Mth. 31 (1900) 60-. 

isomorphic with the simple group of 

order 25920. Dickson, L. E. C. E. 128 
(1899) 873-. 

as quotient groups. Dickson, L. E. 
N. Y. Am. Mth. S. T. 1 (1900) 30-. 

homogeneous group. Dickson, L. E. N. 
Y. Am. Mth. S. Bll. 5 (1899) 120-. 

groups. Taber, H. N. Y. Am. Mth. 

S. Bll. 2 (1896) 336-; 3 (1897) 121. 
defined by an invariant. Dickson, 

L. E. Mth. A. 52 (1899) 560-. 
in a Galois field, etc. Dickson, L. E. 

Am. J. Mth. 21 (1899) 193-. 

substitutions on mq variables, etc. 
Dickson, L. E. L. Mth. S. P. 30 (1899) 
200-. 

substitution groups, coefficients. Maschke, 
H. Mth. A. 50 (1898) 492-. 

and quadratic forms of Dirichlet 
and Hermite. Bianchi, L. Em. E. Ac. 
Line. Ed. 7 (1891) (Sem. 2) 3-. 

substitutions applied to theory of groups. 
Laurent, H. N. A. Mth. 16 (1897) 149-. 

Magic squares, application to group theory. 

Maillet, E. Toul. Ac. Sc. Mm. 6 (1894) 

258-. 

Metacyclic groups and neighbouring configura- 
tions. Heffter, L. Mth. A. 50 (1898) 261-. 
, and triple systems. Heffter, 

L. D. Mth. Vr. Jbr. 5 (1901) (Heft 1) 67-. 
Multiplication forms with application to theory 

of automorphic forms. Ritter, E. Mth. A. 

44 (1894) 261-. 
Non-isomorphic simple groups. Dickson, L. E. 

N. Y. Am. Mth. S. Bll. 6 (1900) 268, 276-. 
Normal divisors of prime index of a finite 

group. Bagnera, G. Em. E. Ac. Line. Ed. 

7 (1898) (San. 1) 63-. 
Number of values a function can take by 

permutation of its letters. Cauchy, A. L. 

Par. EC. Pol. J. 10 (1815) (17 e cah.) 1-; 

C. E. 21 (1845) 593-, 668-, 727-, 779-, 1356-. 
. Spitzer, 

S. [1848] Haidinger Ab. 3 (1850) (Ab. 2 

43-. 
. Serret, 

J. A. Liouv. J. Mth. 15 (1850) 1-. 
. Mathieu, 

E. [1858-59] Liouv. J. Mth. 5 (1860) 9-. 



69 



1210 



Discrete Groups of Finite and of Infinite Order 



Number of values a function can take by 

permutation of its letters. Jordan, C. Par. 

F,c. Pol. J. 22 (1861) (cah. 38) 113-. 
. Gosiewski, 

W. Par. T. Nauk S"c. Pam. 2 (*1872) 1-; 

(x) Bll. Sc. Mth. As. 6 (1874) 154-. 
. Bochert, 

A. Mth. A. 33 (1889) 584-; 40 (1892) 

157-. 
. Carton, 

E. Par. S. Mth. Bll. 22 (1894) 230-. 
. Bochert, 

A. Mth. A. 49 (1897) 113-. 
of rational functions of given number 

of letters, etc. Spina, C. Em. At. N. 

Line. 21 (1868) 182-. 
variables in irreducible group. Molien, 

T. Dorpat Sb. 11 (1896) 277-. 
Octahedron, forms connected with the. 

Pittarelli, G. Em. E. Ac. Line. Ed. 4 

(1888) (San. 1) 509-. 
Operation groups. Cesaro, E. Em. E. Ac. 

Line. Ed. 2 (1886) (Sem. 2) 35-. 
. Le Vavasseur, R. P. C. E. 122 

(1896) 180-, 516-, 711-. 

. Miller, G. A. C. E. 128 (1899) 

227-, 628. 
, generation. Frattini, G. Em. E. Ac. 

Line. Ed. 1 (1885) 281-, 455-; 2 (1886) 

(Sem. 1) 16-. 
of order Sp, p being any prime number. 

Miller, G. A. Ph. Mg. 42 (1896) 195-. 
p a , p being any prime number. 

Miller, G. A. Mess. Mth. 27 (1898) 119-. 

f order less than 64, and order 2p 3 , 
p being prime. Miller, G. A. QJ. Mth. 
30 (1899) 243-. 

, theorems on. Miller, G. A. [1896] N. 

Y. Am. Mth. S. Bll. 3 (1897) 111-. 

symbols involving Galois' imaginaries. 
Le Vavasseur, E. P. Toul. Ac. Sc. Mm. 9 

(1897) 247-. 

Operations, a group of. Brunei, G. Bordeaux 
S. Sc. PV. (1896-97) 30-. 

and substitutions, groups of. Maillet, E. 
As. Fr. C. E. (1897) (Pt. 2) 190-. 

Orthogonal group in a Galois field. Dickson, 

L. E. N. Y. Am. Mth. S. Bll. 4 (1898) 

196-. 
, groups derived from. Dickson, L. E. 

[1898-99] N. Y. Am. Mth. S. Bll. 4 (1898) 

382-, 560 ; Calif. Ac. P. (Mth. Ps.) 1 (1903) 

29-, 47-. 
Perfect groups.- Miller, G. A. Am. J. Mth. 

20 (1898) 277-. 
Permutable substitutions. Baraniecki, M. A. 

Par. T. Nauk Sc. Pam. 7 (*1875) Art. 7, 

35pp. 
Permutants, note. Bilenki, H. N. A. Mth. 

19 (1900) 213-. 
Permutation-groups of 8 things. Wiman, A. 

Gott. Nr. (1897) 55-. 
Permutations, relation between number of 

alternate and quasi-alternate. Andre, D. 

Par. S. Phlm. Bll. 8 (1896) 5-. 
, transformation and classification. Sprague, 

T. B. Edinb. Mth. S. P. 9 (1891) 59-. 



1210 



Position of inflection points in a plane cubic. 

Disteli, M. Ziir. Vjschr. 35 (1890) 145-. 
Possible types of plane quartics, multiply 

homological with themselves. Ciani, E. 

Palermo Cir. Mt. Ed. 13 (1899) 347-. 
Primitive groups. Jordan, C. Liouv. J. Mth. 

16 (1871) 283-; (x) Par. S. Mth. Bll. 1 

(1873) 175-. 

. Rudio, F. Crelle J. Mth. 102 (1888) 1-. 

of class n - 1 and degree n. Maillet, E. 

Par. S. Mth. Bll. 25 (1897) 16-. 
n-2 and degree n. Maillet, E. 

As. Fr. C. E. (1898) (Pt. 2) 157-. 
, classification. Jordan, C. C. E. 73 

(1871) 853-. 
containing a given substitution, limit 

of degree. Jordan, C. C. E. 78 (1874) 

1217- ; Crelle J. Mth. 79 (1875) 248-. 
of degree less than 17, enumeration. 

Miller, G. A. C. E. 124 (1897) 1505- ; 

125 (1897) 673. 

for first 17 degrees, enumeration. 
Jordan, C. C. E. 75 (1872) 1754-. 

, holohedrically isomorphic with groups 

several times transitive. Maillet, E. C. E. 

124 (1897) 351-; Liouv. J. Mth. 3 (1897) 

277-. 
, mode of formation. Maillet, E. QJ. 

Mth. 27 (1895) 119-. 

substitution groups of degree 10, 15, and 
16. Miller, G. A. L. Mth. S. P. 28 (1897) 
533-; Am. J. Mth. 20 (1898) 229-; QJ. 
Mth. 31 (1900) 228-. 

Primitivity of groups. Dyck, W. C. E. 96 
(1883) 1024-. 

and transitivity of discrete group. Dyck, 
W. [1881-82] Mth. A. 20 (1882) 1-; 22 
(1883) 70-. 

Quartic of Klein, theorem concerning. Ciani, 

E. Mil. I. Lomb. Ed. 33 (1900) 565-. 
Quaternary group of 51840 linear substitutions. 

Morrice, G. G. [1889-92] L. Mth. S. P. 

21 (1891) 58-; 23 (1892) 213-. 
substitutions with ternary Hessian 

for sub-group. Maschke, H. Gott. Nr. 

(1888) 78-; Mth. A. 33 (1889) 317-. 

quadratic forms, and polyhedral groups. 
Bianchi, L. A. Mt. 21 (1893) 237-; 23 
(1895) 1-; Em. E. Ac. Line. Ed. 3 (1894) 
(Sem. 1) 3-. 

Quotient G/H in the theory of groups, note 

on so-called. Cayley, A, Am. J. Mth. 15 

(1893) 387-. 
Eational functions, theory. Beke, E. Mth. 

A. 47 (1896) 441-. 
Eeduction of the Galois group of an equation 

by adjunction of arbitrary irrationalities. 

Bucca, F. Palermo Cir. Mt. Ed. 14 (1900) 

122-. 
Eegular substitution groups of order less than 

48. Miller, G. A. QJ. Mth. 28 (1896) 232-. 
Eepresentation, analytical, of substitutions. 

Polignac, C. de. Par. S. Mth. Bll. 9 (1881) 

59-. 
, , for a prime number of elements. 

Grandi, A. G. Mt. 19 (1881) 238-. 
, , , theorem generalised. Grandi, 

A. Mil. I. Lomb. Ed. 16 (1883) 101-. 



70 



Discrete Groups of Finite and of Infinite Order 



1210 



Kesolvable groups. Frobenius, G. Berl. Ak. 

Sb. (1893) 337-; (1895) 1027-. 
Simple group of order 504. Burnside, W. 

Mth. A. 52 (1899) 174-. 
between 1092 and 2001, proof of 

non-existence. Ling, G. H., & Miller, 

G. A. Am. J. Mth. 22 (1900) 13-. 
360 operations. Fricke, E. Gott. 

Nr. (1896) 199-. 
plane collineations. Gerbaldi, F. 

Palermo Cir. Mt. Rd. 12 (1898) 23-; 13 

(1899) 161- ; 14 (1900) 66-. 

homographies. Wiman, A. 
Mth. A. 47 (1896) 531-. 

504 operations. Fricke, R. Mth. A. 
52 (1899) 321-. 

groups, doubly infinite system of. Moore, 
E. H. [1893] N. Y. Mth. S. Bll. 3 (1894) 
73-. 

as far as order 660. Cole, E. N. Am. 

J. Mth. 15 (1893) 303-. 
of order less than 200. Holder, 0. 

Mth. A. 40 (1892) 55-. 

from order 201 to order 500. Cole, 
E. N. Am. J. Mth. 14 (1892) 378-. 

, several classes. Miller, G. A. [1899] 

L. Mth. S. P. 31 (1900) 148-. 
, some. Miller, G. A. Par. S. Mth. 

Bll. 28 (1900) 266-. 

, sub-groups of doubly infinite series. 
Wiman, A. Stockh. Ak. Hndl. Bh. 25 

(1900) (Afd. 1) No. 2, 47 pp. 

, triply infinite system. Dickson, L. E. 
QJ. Mth. 29 (1898) 169- ; 30 (1899) 383-. 

linear groups of order 25920, etc. Dickson, 
L. E. [1899] L. Mth. S. P. 31 (1900) 
30-. 

transitive groups, note on. Miller, G. A. 
[1899] N. Y. Am. Mth. S. Bll. 6 (1900) 
103-. 

600-cell hyper-polyhedron and its self-corre- 
sponding displacements. Oss, S. L. van. 
[1899] Amst. Ak. Vh. (Sect. 1) 7 (1901) 
No. 1, 18 pp. ; Nt. 61 (1899-1900) 304. 

Space, division by linear transformation groups. 
Dyck, W. Leip. Mth. Ps. B. 35 (1883) 61-. 

Special sub-groups of class one. Fricke, R. 
Mth. A. 30 (1887) 345-. 

Sub-groups of the Betti-Mathieu group. 
Dickson, L. E. Am. J. Mth. 22 (1900) 49-. 

llth class in the modular group. 

Rougier, J. Mars. Fac. Sc. A. 6 (1897) 
Fasc. 1, 112 pp. 

Substitution groups. Miller, G. A. C. R. 
122 (1896) 370- ; 123 (1896) 91-, 204. 

. Maillet, E. Par. S. Mth. Bll. 24 

(1896) 85-. 

, composition. Capelli, A. Rm. R. Ac. 

Line. Mm. 19 (1884) 262-. 

whose degree does not exceed eight. 
Miller, G. A. Am. J. Mth. 21 (1899) 287-. 

, general solution of problem of. Hoyer, 

P. Mth. A. 52 (1899) 550-. 

of given order. Maillet, E. Toul. 
Fac. Sc. A. 9 (1895) D, 22 pp. ; 10 (1896) 
A, 20 pp. 

with integral coefficients. Viterbi, A. 

G. Mt. 36 (1898) 346-. 



1210 



Substitution groups whose order = degree. 

Le Vavasseur, R. P. C. R. 120 (1895) 

822-, 899-, 1206- ; 121 (1895) 238-. 
---- is 4. Miller, G. A. Ph. Mg. 

41 (1896) 431-. 
----- the product of two primes. 

Miller, G. A. N. Y. Am. Mth. S. Bll. 2 

(1896) 332-. 

producible from given number of 
elements, list of all. Miller, G. A. N. Y. 
Am. Mth. S. Bll. 2 (1896) 138-. 

-- , theorems on. Sylow, L. Mth. A. 5 

(1872) 584-. 
-- , theory of. Netto, E. Crelle J. Mth. 

103 (1888) 321-. 
-- , , two laws in. Hoyer, B. Mth. A. 

46 (1895) 539-. 
-- for 2, 3, 4, 5, 6, 7 and 8 letters. 

Cayley, A. QJ. Mth. 25 (1891) 71-, 137-. 

, 3, 4, 5, 6 and 7 letters. Askicith, 
E. H. QJ. Mth. 24 (1890) 111-. 

-- of 6, 7 and 8 letters. Cole, F. N. N. 
Y. Mth. S. Bll. 2 (1893) 184- ; 3 (1894) 169. 

-- 8 letters. Askwith, E. H. QJ. 
Mth. 24 (1890) 263-. 

----- . Miller, G. A. N. Y. Mth. 

S. Bll. 3 (1894) 168-. 
---- and 9 letters. Miller, G. A. 

N. Y. Mth. S. Bll. 3 (1894) 242-. 
--- 9 letters. Askwith, (Rev.) E. H. 

QJ. Mth. 26 (1893) 79-. 
----- , list. Cole, F. N. QJ. Mth. 

26 (1893) 372-. 
Substitutions of form 



n being prime. Brioschi, F. Gott. Nr. 
(1869) 491-. 

n letters which leave k letters un- 
altered, number of. Durfee, W. P. J. H. 
Un. Cir. [4] (1885) 23. 

, particularly for n = 3, 4, 5, 6, in 
relation to groups of Pascal's hexagram, 
geometrical interpretation. Veronese, G. 
A. Mt. 11 (1882-83) 93-. 

on p n letters where p is prime. Dickson, 
L. E. A. Mth. 11 (1896-97) 65-, 161-. 

represented by transpositions. Caldarera, 
G. Catania Ac. Gioen. At. 9 (1896) Mm. 7, 
16pp. 

, theorem in. Cayley, A. C.R. 67 (1868) 784-. 

, . Frattini, G. [1884] Rm. R. Ac. 
Line. Mm. 18 (1883) 487-. 

, . Giwlice, F. Palermo Cir. Mt. 
Rd. 1 (1887) 222-. 

, theorems, general. Jordan, C. C. R. 66 
(1868) 836-. 

, theory. Betti, E. Tortolini A. 6 (1855) 5-. 

, . Bachmann, P. Liouv. J. Mth. 10 
(1865) 209-. 

, . Janni, G. G. Mt. 9 (1871) 280- ; 
10 (1872) 193- ; 11 (1873) 1-, 71-, 257-. 

_, _. Jordan, C. G. Mt. 10 (1872) 116; 
Liouv. J. Mth. 17 (1872) 351- ; C. R. 76 
(1873) 952-. 

, , and applications. Netto, E. Arch. 
Mth. Ps. 62 (1878) 225-. 



71 



1210 Discrete Groups 

Substitutions, theory, fundamental theorem, 

new proof. Netto,E. Mth. A. 13 (1878) 249-. 
, (Netto). Miller, G. A. A. Mth. 1 

(1900) 71-. 
, , primitive groups of, etc. Jordan, C. 

C. E. 79 (1874) 1149-. 
Surfaces admitting an infinite discontinuous 

group of transformations. Painleve, P. C.B. 

126 (1898) 512-. 
Sylow's theorem. Frobenius, G. Crelle J. 

Mth. 100 (1887) 179-. 
, application to symmetric group. Eadcig, 

A. A. Kharkov Mth. S. Com. 5 [1896?] 1-. 
, extension. Miller, G. A. N. Y. Am. 

Mth. S. Bll. 4 (1898) 323-. 

, generalisation. Frobenius, G. Berl. 
Ak. Sb. (1895) 981-. 

theorems on groups, illustration. Cayley, 
A. Mess. Mth. 23 (1894) 59-. 

Symmetric and alternant homographic groups. 
Maschke, H. Mth. A. 51 (1899) 253-. 

. Wiman, A. Mth. A. 52 

(1899) 243-. 

permutation-groups of n things. 
Wiman, A. Gott. Nr. (1897) 191-. 

group, note. Burnside, W. [1896] L. 
Mth. S. P. 28 (1897) 119-. 

System of linear forms, theorem on. Frattini, 

G. Bm. B. Ac. Line. Bd. 2 (1886) (Sem. 1) 

132-. 
Systems of groups, fundamental theorem 

relative to two. Cauchy, A. L. C. B. 22 

(1846) 630-. 
Tactic disclosing existence of 4-valued function. 

Sylvester, J. J. Ph. Mg. 21 (1861) 515-. 
Ternary substitution-groups of finite order, 

which leave a triangle unchanged. Maschke, 

H. Am. J. Mth. 17 (1895) 168-. 
Theta-fuchsian functions. Ovidio, E. d\ 

Tor. Ac. Sc. At. 29 (1894) 741-. 
Transitive functions, reduction to intransitive. 

Cauchy, A. L. C. E. 21 (1845) 1199-. 

group, G120 of six letters, invariant functions. 
Dziobek, 0. Arch. Mth. Ps. 68 (1882) 225-. 

Transitive groups. Maillet, E. A. Mt. 25 

(1897) 219-. 
of degree n and class n- 1. Maillet, E. 

Par. S. Mth. Bll. 26 (1898) 249-. 

whose degree is the square of a prime. 
Sylmv, L. Acta Mth. 11 (1887-88) 201-. 

isomorphic to alternating group of six. 

Miller, G. A. Am. Ph. S. P. 36 (1897) 208-. 
, proofs and theorems. Netto, E. Crelle 

J. Mth. 83 (1877) 43-. 

substitution groups. Bochert, A. Mth. A. 
40 (1892) 176- ; 49 (1897) 133-. 

. Miller, G. A. Mess. Mth. 28 

(1899) 84-. 
of degree 12. Miller, G. A. N. Y. 

Am. Mth. S. Bll. 1 (1895) 255-. 
, list. Miller, G. A. QJ. 

Mth. 28 (1896) 193-. 
13 and 14. Miller, G. A. 

QJ. Mth. 29 (1898) 224-. 
17. Miller, G. A. QJ. Mth. 

31 (1900) 49-. 
isomorphic to a given group. Miller, 

G.A. G. Mt. 38 (1900) 63-. 



Continuous Groups 1230 

Transitive substitution groups of nine letters. 

Cole, F. N. N. Y. Mth. S. Bll. 2 (1893) 

250-. 
10 and of 11 letters, list. Cole, 

F. N. QJ. Mth. 27 (1895) 39-. 
24 letters, etc. Wilkinson, A.C.L. 

QJ. Mth. 30 (1899) 157-. 

whose order is the cube of any 
prime: the non-regular. Miller, G. A. A. 
Mth. 10 (1895-96) 156-. 

product of three primes: 
the non-regular. Miller, G.A. Zttr. Vjschr. 
42 (1897) 68-. 

of order 8p, p being any prime. 
Miller, G. A. Ph. Mg. 43 (1897) 117-. 

whose orders are products of three 

primes. Miller, G. A. N. Y. Am. Mth. S. 

Bll. 3 (1897) 213-. 
of same order and degree. Frattini, 

G. Em. E. Ac. Line. At. 14 (1883) 143-. 
Triple systems. Moore, E. H. Mth. A. 43 

(1893) 271- ; Palermo Cir Mt. Ed. 9 (1895) 

86. 

. Heffter, L. Mth. A. 49 (1897) 101-. 

. Moore, E. H. N. Y. Am. Mth. S. Bll. 

4 (1898) 11-. 
, theory. Netto, E. Mth. A. 42 (1893) 

143. 
, . Vries, J. de. Palermo Cir. Mt. Ed. 

8 (1894) 222-. 
, transitive. Moore, E. H. Mth. A. 50 

(1898) 225-. 

tangent planes of cubic surface, proof of 
Cayley's theorem. Kohn, G. Mh. Mth. Ps. 
2 (1891) 343-. 

Two groups in five dimension space. Engel, F. 

D. Mth. Vr. Jbr. 8 (1900) (Heft 1) 196-. 
Uniform group and linear transformation. 

Kneser, A. Mth. A. 28 (1887) 125-. 
Universal invariant for finite groups of linear 

substitutions. Moore, E. H. Mth. A. 50 

(1898) 213-. 

1230 Continuous groups of finite 
and of infinite order. 

Algebraic groups, certain. Cartan, E. C. B. 

120 (1895) 544-. 
of straight lines and planes. Carda, K. 

Mh. Mth. Ps. 11 (1900) 31-. 

surfaces admitting continuous transitive 
group of transformations. Fano, G. Palermo 
Cir. Mt. Bd. 10 (1896) 1-. 

with continuous group of birational trans- 
formations into them selves. Castelnuovo, G., 
<& Enriques, F. C. E. 121 (1895) 242-. 

. Painleve, P. 

C. E. 121 (1895) 318-. 

infinite automorphic transformations. 

Enriques, F. Yen. I. At. (1892-93) 1590- ; 
(1893-94) 638-. 

. Fano, G. Em. E. Ac. 

Line. Ed. 4 (1895) (Sem. 1) 149- ; Palermo 
Cir. Mt. Bd. 11 (1897) 240-. 

Canonical form, reduction of finite and con- 
tinuous group of transformations to. Cartan, 
E. Am. J. Mth. 18 (1896) 1-. 



72 



1230 Continuous Groups of Finite and of Infinite Order 1230 



Canonical form, reduction of group of trans- 
formations to. Lie, S. Leip. Mth. Ps. B. 
41 (1889) 277-. 

Complex numbers and groups of transforma- 
tions. Study, E. Leip. Mth. Ps. B. 41 
(1889) 177. 

, systems of, and transformation groups. 

Study, E. Mh. Mth. Ps. 1 (1890) 283-. 

Conformal representation; Poincare's theory; 
substitution groups. Brun, F. de. Stockh. 
Ofv. (1890) 135- ; Fschr. Mth. (1890) 410. 

Contact transformations, finite groups contained 
in the group of linear. Autonne, L. C. E. 
102 (1886) 313-. 

, irreducible groups. Lie, S. Leip. Mth. 

Ps. B. 41 (1889) 320-. 

, theory. Lie, M. S. Arch. Mth. Ntvd. 

1 (1876) 194-. 

Continuity of infinitesimal transformation 
groups. Slocum, S. E. Am. Ac. P. 36 
(1901) 83-. 

Continuous binary linearoid groups, and corre- 

rnding differential equations. Wilczynski, 
J. Am. J. Mth. 22 (1900) 191-. 

and discontinuous groups, correspondence 
between. Bettazzi, R. A. Mt. 16 (1888-89) 
49-. 

group of Darboux rotations. Souslow, G. 
D. Nf. Vh. (1895) (Th. 2, Hfilfte 1) 12-. 

defined by any given group of finite 
order. Burnside, W. L. Mth. S. P. 29 



(1898) 207-, 546-. 
of Jc 



lonquieres' transformations in a plane. 
Enriques, F. Em. E. Ac. Line. Ed. 2 (1893) 
(Sem. 1) 532-. 

in three dimensions. Bianchi, L. Em. 

S. It. Mm. 11 (1898) 267-. 

of transformations with 28 parameters in 
theory of deformation of surfaces. Staeckel, 
P. C. E, 121 (1895) 396-. 

groups. Lie, S. Christiania F. (1884) 
No. 8, 4 pp., No. 9, 4 pp. ; (1885) No. 15, 
4 pp. 

. Poincare, H. C. E. 128 (1899) 1065- ; 

Camb. Ph. S. T. 18 (1900) 220-. 

, application to singular points of differen- 
tial equations. Marotte, F. C. E. 123 (1896) 
867-. 

, theory of functions. Lie, S. C. E. 

114 (1892) 334-. 

, . Painleve, P. C. E. 

118 (1894) 845-. 

and differential equations with fixed 
critical points. Painleve, P. C. E. 130 
(1900) 1171-. 

, Lie's, application. Autonne, L. C. E. 

112 (1891) 570-. 
, theory. Lovett, E. 0. [1897] N. Y. 

Am. Mth. S. Bll. 4 (1898) 59-. 
, . Slocum, S. E. Am. Ac. P. 35 

(1900) 237-, 481-. 
, . Eettger, E. W. Am. J. Mth. 22 

(1900) 60-. 
, , application. Drach, . C. E. 

116 (1893) 1041-. 
, problems in theory. Bouton, C. L. A. 

Mth. 1 (1900) 93-. 



Continuous groups of projective transforma- 
tions. Newton, H. B. [1895-96] Kan. Un. 
Q. 4 (1896) 71-, 169-, 243-; 5 (1896) 
81. 

quadratic transformations of the 
plane. Bohlmann, G. Gott. Nr. (1896) 

in space of n dimensions, determination. 

Medolaghi, P. Em. E. Ac. Line. Ed. 8 
(1899) (Sem. 1) 291-. 

, theorem in. Koch, H. von. Stockh. 
Ofv. (1894) 311-. 

, theory. Campbell, J. E. N. Y. Am. 

Mth. S. Bll. 4 (1898) 407-. 

imprimitive groups of point transformations. 
Fano, G. Em. E. Ac. Line. Ed. 7 (1898) 
(Sem. 1) 302- . 

Cremona cubic group, finite groups. Autonne, 
L. C. E. 101 (1885) 53-; 105 (1887) 267-. 

group with any number of variables, com- 
plete groups contained in a. Del Re, A. 
Em. E. Ac. Line. Ed. 6 (1890) (Sem. 2) 
271-. 

, finite groups in. I. Quadratic groups. 

II. Cubic groups. Autonne, L. Liouv. J. 
Mth. 1 (1885) 431- ; 2 (1886) 49-. 

quadratic group, finite groups in. Autonne, 
L. C. E. 98 (1884) 565-; Liouv. J. Mth. 4 
(1888) 177-, 407-. 

, irreducible groups of finite order in. 

Autonne, L. C. E. 103 (1886) 1176-. 
groups. Autonne, L. C. E. 104 (1887) 

1422-. 

transformations, continuous groups of. 
Noether, M. D. Nf. Vh. (1896) (Th. 2, 
Halfte 1) 11-. 

, . Fano, G. Mh. Mth. Ps. 9 



in plane, continuous groups of. 
Enriques, F. Em. E. Ac. Line. Ed. 2 
(1893) (Sem. 1) 468-. 

, , and certain projective 

transformation groups. Fano, G. Palermo 
Cir. Mt. Ed. 10 (1896) 16-. 

of space, continuous primitive groups of. 

Fano, G. Tor. Ac. So. At. 33 (1897) 284- or 

480-. 
Differential equations admitting finite groups. 

Lie, S. Mth. A. 25 (1885) 71-. 
a group of transformations. Lie, S. 

Arch. Mth. Ntvd. 9 (1884) 431-. 

infinitesimal transformations. 
Paczmvski, J. Prace Mt.-Fiz. 7 (1896) 
178-. 

, algebraic and group theory. Loewy, A. 

Mh. Mth. Ps. 8 (1897) 225-. 

which possess fundamental integrals. 
Lie, S. Leip. Mth. Ps. B. 45 (1893) 
341-. 

invariants of equation of 2nd order. 
Tresse, A. Leip. Jablon. Preisschr. 32 
(1896) 87 pp. 

Dynamical problems, whose solutions admit of 

infinitesimal transformation. Stackel, P. 

Leip. Mth. Ps. B. 45 (1893) 331-. 
Dynamics, differential equations of, application 

of Lie's transformation guoups. Stackel, P. 

Leip. Mth. Ps. B. 49 (1897) 411-. 



73 



1230 Continuous Groups of Finite and of Infinite Order 1230 



Finite continuous group of transformations, 

investigation of the finite equations of a. 

Vessiot, E. Toul. Fac. Sc. A. 10 (1896) C, 

26pp. 
groups. Autonne, L. Liouv. J. Mth. 3 

(1887) 63-. 

, complete systems and differential 

invariants of. Lindelof, E. Helsingf. Acta 

20 (1895) No. 1, 62 pp. 
, determination of equations. Vessiot, 

E. C. R. 120 (1895) 77-. 

of Lie's transformations, decom- 
position. Maillet, E. C. E. 130 (1900) 
1536^. 

the plane. Williams, F. B. Am. 

Ac. P. 35 (1900) 95-. 
, structure. Cartan, . C. E. 116 

(1893) 962-. 
of transformations. Engel, F. Leip. 

Mth. Ps. B. 38 (1886) 83-. 
primitive groups of Lie's transformations. 

Maillet, E. C. E. 130 (1900) 1602-. 

transformations of a projective group, gene- 
rated by the infinitesimal transformations of 
the group. Engel, F. Leip. Mth. Ps. B. 44 
(1892) 279-; 45 (1893) 659-. 

General projective group, case of degeneration. 

Engel, F. C. E. 118 (1894) 397-. 
Geometry of functional space. Pincherle, S. 

Bologna Ed. 1 (1897) 85-. 
Greatest continuous groups of certain systems 

of differential equations, finite character. 

Engel, F. Leip. Mth. Ps. B. 46 (1894) 

297-. 
Group and invariant, the conceptions. Lie, S. 

Leip. Mth. Ps. B. 39 (1887) 83-. 

of parameters, canonical form. Schur, F. 
Leip. Mth. Ps. B. 41 (1889) 229-. 

theory applied to hydrodynamics. Wilczyn- 
ski, E. J. N. Y. Am. Mth. S. T. 1 (1900) 
339-, 509. 

for equations of the 2nd degree with n 

variables. Werner, H. Mth. A. 35 (1890) 

113-. 
, geometrical treatment. Paolis, R. de. 

Em. S. It. Mm. 7 (1890) No. 6, 164 pp. 
, minor contributions. Engel, F. Leip. 

Mth. Ps. B. 39 (1887) 89-; 43 (1891) 47-, 

308-, 585-; 44 (1892) 43-, 292-; 45 (1893) 

360- ; 46(1894)25-. 
, recent investigations. Lie, S. Leip. 

Mth. Ps. B. 44 (1892) 297-. 
Groups and algebraic surfaces. Picard, E. 

Palermo Cir. Mt. Ed. 9 (1895) 244-. 

appearing in the theory of analytical func- 
tions. Medolaghi, P. C. E. 126 (1898) 
1188-. 

of circular transformations. Newson, H. B. 
[1897] N. Y. Am. Mth. S. Bll. 4 (1898) 

isomorphous to the group of all the trans- 
formations of one variable. Medolaghi, P. 
Palermo Cir. Mt. Ed. 12 (1898) 188-. 

Hyperfuchsian groups. Poincare, H. C. E. 

98 (1884) 503-. 
Infinite continuous groups. Lie, M. S. Chris- 

tiania F. (1883) No. 12, 56 pp. ; Leip. Mth. 

Ps. Ab. 21 (1895) 43-. 



Infinite continuous groups, theory. Medolaghi, 

P. A. Mt. 25 (1897) 179-. 
of transformations, foundations of 

theory. Lie, S. Leip. Mth. Ps. B. 43 (1891) 

316-, 353-. 

groups, theorem concerning. Lie, S. 
Christiania F. (1889) No. 7, 6 pp. 

of transformations. Tresse, A. C. E. 

115 (1892) 1003-. 
, and integration of differential 

equations. Beudon, J. C. E. 125 (1897) 

811-. 

ternary automorphic transformations, theo- 
rem on. Fano, G. Em. E. Ac. Line. Ed. 8 
(1899) (Sem. 1) 562-. 

Infinitesimal automorphic transformations of 
a Pfaffian equation. Vivanti, G. Palermo 
Cir. Mt. Ed. 12 (1898) 1-. 

. Weber, E. von. Palermo 

Cir. Mt. Ed. 12 (1898) 133-. 

groups, singular transformations. Taber, H. 
Am. Ac. P. 35 (1900) 575-. 

transformations of all transitive finite 
groups, given by quotients of power series. 
Schur, F. Leip. Mth. Ps. B. 42 (1890) 1-. 

Integral invariants of continuous transforma- 
tion groups. Zorawski, K. Krk. Ak. (Mt.- 
Prz.) Ez. 8 (1895) 232-; Crc. Ac. Sc. Bll. 
(1895) 127-. 

Integrals of canonical system, group interpre- 
tation. Levi-Civita, T. Em. E. Ac. Line. 
Ed. 8 (1899) (Sem. 2) 235-. 

Invariant theory of group of motions. Lie, S. 
Leip. Mth. Ps. B. 48 (1896) 466-. 

Invariants of conies and quadric surfaces given 
by motion and similitude groups. Lovett, 
E. O. A. Mth. 11 (1896-97) 33-. 

Isomorphic groups of substitutions with sym- 
metric or alternate groups. Maillet, . 
C. E. 119 (1894) 362-. 

Jonquieres groups, generalised. Fano, G. 
[1898] Tor. Ac. Sc. Mm. 48 (1899) 221-. 

Kummer's configuration, and orthogonal sub- 
stitutions. Study, E. Leip. Mth. Ps. B. 44 
(1892) 122-. 

Linear differential equations. Lie, S. Chris- 
tiania F. (1885) No. 21, 4 pp. 

, groups of transformations. Picard, E. 

C. E. 119 (1894) 584-. 

equations, groups. Poincare, H. Acta 
Mth. 4 (1884) 201-. 

homogeneous continuous groups. Maurer, L. 
Munch. Ak. Sb. 24 (1895) 297-. 

whose operations are permutable. 

Burnside, W. L. Mth. S. P. 29 (1898) 325-. 
group with invariant Pfaffian. Dickson, 

L. E. N. Y. Am. Mth. S. Bll. 5 (1899) 

338-. 

partial differential equations with continuous 
transformation group. Campbell, J. E. N.Y. 
Am. Mth. S. T. 1 (1900) 243-, 509. 

Monomial group associated with an infinitesimal 
projective transformation. Torelli, G. Pa- 
lermo Cir. Mt. Ed. 8 (1894) 41-. 

Ordinary differential equations which have 
fundamental systems of integrals. Lie, S. 
C. E. 116 (1893) 1233-. 



74 



1230 Continuous Groups 

mn 2 Parameter group in mn variables. Wil- 
czynski, E. J. [1899] Calif. Ac. P. (Mtk.-Pt.) 
1 (1903) 59-. 

Parametric groups in the theory of linear sub- 
stitutions. Maillet, E. A. Mt. 23 (1895) 199-. 

Partial differential equations of 1st order, 
singularities. Marotte, F. C. B. 123 (1896) 
933-. ' 

with two independent 
variables, admitting a continuous group of 
transformations. Tannenberg, W. de. Toul 
Fac. Sc. A. 5 (1891) B, 150pp. 

Point-aggregate, doubly extended, determina- 
tion of all groups of. Lie, M. S. Arch. 
Mth. Ntvd. 3 (1878) 93-. 

Primitive transformation groups in five 
variables. Kowalewski, G. Leip. Mth. Ps 
B. 51 (1899) (Mth.) 69-. 

Projective group. Eettger, E. W. Am. Ac. P. 
33 (1898) 491-. 

Properties of groups of substitutions of given 
order. Maillet, E. C. B. 118 (1894) 1187-. 

Simple finite continuous groups, structure. 
Cartan, . C. B. 116 (1893) 784-. 

group with 14 parameters. Engel, F. C. B. 
116 (1893) 786-. 

Simply infinite continuous protective groups in 
ordinary space. Pittarelli, G. A. Mt 22 
(1894) 261-. 

Simultaneous differential equations with con- 
tinuous transformation groups. Zindler, K. 
Mh. Mth. Ps. 11 (1900) 289-. 

Structure of a group, reduction to canonical 
form. Cartan, E. C. B. 119 (1894) 639-. 

Sub-groups of a group of Lie's transformations. 
Maillet, E. C. B. 130 (1900) 1449-. 

Substitutions, groups of, special class. Ahrens, 
W. Leip. Mth. Ps. B. 49 (1897) 616-. 

Systems of partial differential equations de- 
fining a group. Medolaghi, P. Bm. B. Ac. 
Line. Bd. 6 (1897) (Sem. 1) 575-. 

Transformation, general theory. Lie, S. 
Leip. Mth. Ps. B. 40 (1888) 14-. 

groups. Lie, M. S. Gott. Nr. (1874) 
529-. 

. Page, J. M. A. Mth. 8 (1893-94) 

applied to ordinary differential equations. 

Page, J. M. A. Mth. 9 (1894-95) 59-. 
, determination of all transitive, with r 

terms. Lie, S. Leip. Mth. Ps. B. 42 (1890) 

478-. 
, new proof of fundamental theorem in 

theory of. Lie, S. Leip. Mth. Ps. B. 42 

(1890) 453-. 
, researches. Lie, S. Arch. Mth. Ntvd. 

10 (1886) 74-, 353-. 
, simple. Cartan, E. Leip. Mth. Ps. B. 

45 (1893) 395-. 
in space of four dimensions. Page, J. M. 

A. Mth. 9 (1894-95) 11-. 
. West/all, J. V. N. Y. 

Am. Mth. S. Bll. 6 (1900) 185, 191-. 
, theory. Lie, M. S. Arch. Mth. Ntvd. 

1 (1876) 19-, 152- ; 3 (1878) 93-, 375-; 4 

(1879) 232-; 9 (1884) 449-; Mth. A. 16 

(1880) 441- ; Christiania F. (1888) No. 13, 
8 pp. ; Leip. Mth. Ps. B. 46 (1894) 322-. 



Algebra. General 1590 

Types of line-sphere transformation. Lovett, 
E. O. [1900] N. Y. Am. Mth. S. Bll. 7 
(1901) 203, 209-. 

ALGEBRA AND THEORY OF 
NUMBERS. 

1590 General. 

Algebra, pure and applied, exercises. Piani, D. 
[1846-47] Bologna N. Cm. 10 (1849) 571-. 

Algebraic keys. Cauchy, A. L. C. B. 36 
(1853) 70-, 129-, 161-. 

, employment of differentials and varia- 
tions. Cauchy, A. L. C. B. 37 (1853) 38-, 
57-. 

Interpretation of algebraic results. Parker, 
W. H. Camb. (M.) Mth. M. 1 (1859) 

(Parker). Eunkle, J. D. Camb. 

(M.) Mth. M. 1 (1859) 178-. 

Elements of Algebra. 
1600 General. 

Algebra, elementary developments. Finlay, E. 

Mathematician 3 (1850) 291-. 
, , theorem. Marcolongo, E. G. Mt. 25 

(1887) 174-. 
, elements (Lacroix). Oken, L. Oken Isis 

(1825) 1153-. 
, foundation. De Morgan, A. [1839-44] 

Camb. Ph. S. T. 7 (1842) 173-, 287-; 

8 (1849) 139-, 241-. 
, foundations. Sexe, S. A. N. Mg. Ntvd. 

(1866) 1-. 
, , supplementary to Cauchy. Bellavitis, 

G. A. Sc. Lomb. Yen. 1 (1831) 271-. 
, fundamental notions. Ballauff,L. Grunert 

Arch. 5 (1844) 259-. 
, laws. De Morgan, A. (ix) [1853] Camb. 

Ph. S. P. 1 (1866) 123-. 
, principles. Paque,A.J.N. (vm) Liege 

Mm. S. Sc. 18 (1863) 93-. 
,, first. Schulten,N.G.af(fil). Helsingf. 

Acta 1 (1840) 395-. 
, , . Moigno, F. Les Mondes 3 (1863) 

254-, 269-, 318-, 358-, 605-, 635-. 
, , fundamental. Schulten, N. G. af (fil). 

[1839] Helsingf. Acta 1 (1840) 31-. 
, , . Petersen, J. Ts. Mth. 3 (1885) 1-; 

Fschr. Mth. (1885) 123. 

Algebraic analysis and the factorial interpreta- 
tion of powers. Capelli, A. G. Mt. 31 

(1893) 291-, 340- ; 33 (1895) 361-. 

calculation. Franchini, P. Lucca At. Ac. 
2 (1823) 193-. 

, exercises. Eealis, S. N. A. Mth. 20 

(1881) 501-. 

formulae treated geometrically. Lucas, E. 
As. Fr. C. E. (1885) (Pt. 1) 94. 

and goniometric identities, development of 
some. Berg, F. J. van den. Amst. Ak. Vs. 
M. 14 (1879) 340-. 



75 



1600 Algebra. General 

Algebraic quantities, principles of an arith- 
metical theory of. Kronecker, L. [1881] 
Crelle J. Mth. 92 (1882) 1-. 

Algorithm [a be ... l]<"\ Ocagne, M. d'. N. A. 
Mth. 5 (1886) 257-. 

of arithmetical means of products of k 
numbers, taken r at a time. Stieltjes, T. J. 
(jun.). Crelle J. Mth. 89 (1880) 343-. 

, elementary, theory. Simdes Margiochi, F. 
Lisb. Ac. Sc. Mm. (Cor.) 3 (pte. 2) (1814) 
27-. 

for geometric mean of n quantities. Stiel- 
tjes, T. J. (jun.) N. Arch. Wisk. 9 (*1882) 
198-. 

Algorithms of algebra. Se'guin, (aine). Moigno 
An. Cosmos (1861) 379-. 

and calculi. Schroeder, E. Arch. Mth. Ps. 
5 (1887) 225-, vii-. 

Approximations, algebraic. Hermite, C. Crelle 

J. 76 (1873) 342-. 
, calculation (in inserting geometric means). 

Duterme, . N. A. Mth. 4 (1845) 124-. 
Arithmetical progressions, new theorem. Jof- 

froy, J. N. A. Mth. 8 (1889) 85-. 
Decomposition of fractions, problem. Jacobi, 

C. G. J. Crelle J. 5 (1830) 344-. 
Development in ascending powers of x of 

l/Za r x r . Gambioli,D. G. Mt. 30 (1892) 35-. 

of numerical quantities analogous to that by 
continued fractions. Cohen, E. N. A. Mth. 
10 (1891) 508-. 

(l + ri*x)". Cayley, A. Mess. Mth. 22 

(1893) 186-. 
Developments of algebraic products. Laisant, 

C. A. As. Fr. C. K. (1881) 84-. 
Equalities in two or three degrees. Frolov, M. 

Par. S. Mth. Bll. 17 (1889) 69-; 20 (1892) 

69-. 
Exponents of any order, theory. Terquem, 0. 

N. A. Mth. 6 (1847) 106-. 
, fractional. Almqvist, P. W. Ts. Mt. Fys. 

1 (1868) 264-. 
, laws. Clauten, T. Crelle J. 7 (1831) 

234-. 

Fraction - , expression as sum of aliquot parts 

of unity. Collignon, E. [1881] Par. S. 

Phlm. Bll. 6 (1882) 88-. 
Harmonic relations. Hultman, F. W. Ts. 

Mt. Fys. 4 (1871) 153-. 
Harmony, algebra of. Loquin, A. Bordeaux 

Ac. Act. 43 (1883) (Suppl.) 1-. 
Identities. Hunyady, E. von. Z. Mth. Ps. 12 

(1867) 89-. ' 
Identity, algebraic. MacMahon, (Capt.) P. A. 

Mess. Mth. 13 (1884) 142-. 

connected with theory of parallels. Mal'tsev, 
M. M. (xn) [1883] Kazan S. Nt. (Ps.- 
Mth.) P. 2 (1884) 8. 

Index law. Hultman, F. W. Ts. Mt. Fys. 3 

(1870) 250-. 
Indices, theory. Sexe, S. A. N. Mg. Ntvd. 

13 (1864) 155-. 
, . Faure, H. N. A. Mth. 15 (1876) 251-, 

292-, 339-, 451-, 481-, 529-; 16 (1877) 5-, 

160-, 193-, 249-, 289-, 467-, 508-, 541- ; 17 

(1878) 69-. 



Algebra. General 1600 

Infinity and sign of equality. De Morgan, A. 

Camb. Ph. S. T. 11 (Pt. I) (1866) 145-. 
Limits of the expression (x? -yP)/(x q -y' 1 ). 

Knight, S. E. Mess. Mth. 22 (1893) 

165-. 
. Segar, H. W. Mess. Mth. 23 

(1894) 47-. 
Maximum of product of positive numbers whose 

sum is given. Darboux, G. Bll. Sc. Mth. 

11 (1887) 149-. 
value of xy when x + y is given. Steiner, J. 

Crelle J. 40 (1850) 208. 
. Oettinger, L. Crelle 

J. 57 (1860) 90-. 
Mean, arithmetic, error due to its substitution 

for geometric mean. Dostor, G. Arch. Mth. 

Ps. 63 (1879) 220. 
, and geometric. Liouville, J. Liouv. 

J. Mth. 4 (1839) 493-. 
, , comparison. Hurwitz, A. Crelle 

J. Mth. 108 (1891) 266-. 

, , difference, and theorem of in- 
tegral calculus. Unferdinger, F. Wien Sb. 

56 (1867) (Ab. 2) 272-. 
, , greater than geometric: mean of m 

numbers (Cauchy). Transon,A. N.A.Mth. 

11 (1872) 257-. 

, , , proof. Thacker, A. Camb. 

and Dubl. Mth. J. 6 (1851) 81-. 
, , , . Tait, P. G. [1868] Edinb. 

B. S. P. 6 (1869) 309. 
, arithmetico -geometric, of 4 elements. 

Borchardt, C. W. Berl. Ak. Mb. (1876) 

611-. 
Means, arithmetic. Lobatto, E. (vm) Quetelet 

Cor. Mth. 4 (1828) 169-, 233-. 
, , geometric and harmonic. Brandli, H. 

Bern Mt. (1849) 178-. 
, , , comparison. Schlomilch, 0. 

Schlomilch Z. 3 (1858) 187-. 
, , of powers of positive quantities. Bien- 

ayme, J. Par. S. Phlm. PV. (1840) 67-. 
, calculation. Laroque, F. Toul. Mm. Ac. 

6 (1862) 295-. 
, a succession of. Neuberg, J. Liege S. Sc. 

Mm. 11 (1885) No. 5, 12 pp. 
Modular systems, applications to elementary 

algebra. Netto, E. Crelle J. Mth. 104 

(1889) 321-. 

Monomial coefficients and coefficients of fac- 
torials. Zeipel, E. V. von. Lund Acta Un. 

6 (1869) (Mth.) No. 3, 57 pp. 
Multiplication, algebraic. Englefield, H. C. 

Tilloch Ph. Mg. 45 (1815) 15-. 
, . Dillon, J. Tilloch Ph. Mg. 45 (1815) 

137-. 
by fractions, interpretation, and principle of 

permanence of equivalent forms. Taylor, C. 

Mess. Mth. 4 (1868) 159-. 
(x + a). Andre, D. Par. EC. Norm. A. 

12 (1883) (Suppl.) 3-. 

(x-a). Andre, D. Par. EC. Norm. A. 

12 (1883) (Suppl.) 33-. 

Negative quantities and rule of signs. Guillon, 
E. L. N. A. Mth. 8 (1849) 28-. 

in solution of equation problems. Green- 
field, W. [1784] Edinb. B. S. T. 1 (1788) 
131-. 



76 



1600 Algebra. General 

Nomography, problem of algebra relating to. 

Ocagne, M. d'. N. A. Mth. 12 (1893) 469-. 
Notation, algebraic. Collins, J. V. Science 

20 (1892) 359. 
, and fluxional, principles. Young, Dr T. 

QJ. Sc. 20 (1826) 321-. 

for printing complicated exponents. Glaisher, 
J. W. L. [1872] Mess. Mth. 2 (1873) 107-. 

Order of factors immaterial. Gergonne, J. D. 

Gergonne A. Mth. 1 (1810-11) 52-. 
Principles, doubtful points. Gyory, S. (xn) 

Mag. Ak. fits. (Mth. Term.) 1 (1860) 287-. 
, three which connect algebra with other 

mathematics. Chelini, D. Palomba Eac. 

2 (1846) 57-, 73-. 
Problem on a cask of brandy, a given quantity 

being withdrawn daily, and lighter spirit 

added. Niirnberger, . Baumgartner Z. 

4 (1828) 76-. 
. Persons in a circle passing money to one 

another. Allegret, A. N. A. Mth. 16 (1857) 

136-. 

. Smallest number of weights needed. Ger- 
gonne, J. D. Gergonne A. Mth. 8 (1817-18) 

305-. 
Problems in Nouv. Ann. Mth. Bellavitis, G. 

Yen. At. 4 (1853) 79- ; (1860) 165-. 

for schools. Dienger, J. Grunert Arch. 9 
(1847) 113-. 

Product of n factors, transformation. Tardy, P. 
Tortolini A. 2 (1851) 287-. 

two algebraic expressions. Elliott, J. 
Mth. Gz. 1 (1900) 187-. 

Proportions and progressions. Vecchio, A. G. 

Mt. 7 (1869) 43-. 
Quadratic expressions, theorem. Lamb, H. 

[1880J Mess. Mth. 10 (1881) 35-. 
Radicals, extraction by binomial theorem and 

Lambert's formula, accuracy. Schulz von 

Strasnzitzki, L. C. Baumgartner Z. 6 (1829) 

31-. 
Rationalisation. Herth, G. (vi. Adds.) D. 

Nf. Vsm. B. 34 (1858) 105. 
, case. Ward, P. C. Mess. Mth. 15 (1886) 

42-. 

of denominators. Grebe, E. W. Grunert 
Arch. 13 (1849) 68-. 

. Zehfuss, G. Grunert Arch. 35 (1860) 

117-. 

. Janisch, E. Arch. Mth. Ps. 10 

(1891) 420-. 

, note. MacMahon, (Capt.) P. A. Mess. 
Mth. 15 (1886) 65-. 

Ratios of k quantities, approximate representa- 
tion by ratios of simple integers. Oliver, J. E. 
[1864] Am. Ac. P. 6 (1866) 288-. 

Reduction of Fahrenheit to centigrade. Tiberi, 
E. Ev. Sc.-Ind. 30 (1898) 216-. 

Va + N/6 to the sum of two squares. 
Schmidt, E. Ts. Mth. 2 (1884) 154-; Fschr. 
Mth. (1884) 146. 

Roots, elementary theory. Baltzer, E. Grunert 
Arch. 18 (1852) 405-. 

of higher degree analogous to B + A \/a. 
Grebe, E. W. Grunert Arch. 13 (1849) 400-. 

Rule of three, theory. Gergonne, J. D. Ger- 
gonne A. Mth. 7 (1816-17) 117-. 



Rational polynomials 1610 

Sign, doubtful, in algebraic formulae, meaning. 
Stevelly, J. B. A. Rp. (1836) (pt. 2) 5-. 

-symbols, theorems relating to. Cayley, A. 
Mess. Mth. 2 (1873) 17-. 

Signs. Schellbach, C. H. Crelle J. 12 (1834) 
70-, 148-. 

. Transon, A. N. A. Mth. 6 (1867) 289-. 

, influence in mathematics. Babbage, C. 
[1821] Camb. Ph. S. T. 2 (1827) 325-. 

, + and - , significance. Purgotti, S. Pal- 
omba Rac. 3 (1847) 265-, 285-, 324-. 

, , , algebraic. Massini, L. Pal- 
omba Rac. 1 (1845) 73-. 

, , before radical ,J . Judson, C. H. 

Des Moines Anal. 2 (1875) 70-. 

Simplification of an algebraic expression. 
Langley, E. M. Mth. Gz. 1 (1900) 129. 

Square root of A+*JB. Gopel, A. Grunert 
Arch. 3 (1843) 249 

quadrinomial surd. Bierens de Haan, 

D. N. Arch. Wisk. 3 (*1877) 208-. 

, test for recognizing whether operations 

va*Jvb>Jwi etc. can be effected under 

form a\/v/3\/wi. Weichold, G. C. R. 96 

(1883) 835-. 
Surd Va <Jb, explanation of Euler's objection 

to Newton's rule for extraction of root. 

Plana, G. Crelle J. 17 (1837) 331- ; 20 (1840) 

283-. 
, extraction of root. Plana, G. N. A. 

Mth. 7 (1848) 271-. 

Surds. Reduction of \/a + Wc to m + nVc. 

Kausler, C. F. [1806] St Pet. Ac. Sc. Mm. 

2 (1810) 64-. 
, theorems. Treuil, . Gergonne A. Mth. 

12 (1821-22) 104-. 
Symbol, new. Whitworth, W. A. Mess. Mth. 

5 (1871) 121. 
Symbols, algebraic. Baker, A. L. Am. J. 

Mth. 18 (1896) 62-. 
, new algebraic, in Phil. Trans. 1862. Drach, 

S. M. (vn) Ph. Mg. 26 (1863) 406-. 
Theory of algebra, from arithmetical principles, 

and nature of signs, etc. Glcesener, M. Liege 

A. Ac. (1818-19) 64 pp. 
Variations and combinations with fixed totals. 

Reich, K. Arch. Mth. Ps. 11 (1892) 225-. 
Viete, Francois, new algebra of. Eitter, F. 

As. Fr. C. R. (1892) (Pt. 2) 177-. 



1610 Rational polynomials; 
divisibility ; reducibility. 

Algebraic calculation and division. Zmurko, W. 

Krk. Ak. (Mt.-Prz.) Pam. 12 (1886) (1)-; 

Fschr. Mth. (1886) 120. 

Approximate expressions, linear in two poly- 
nomials. Cebysev, P. St Pet. Ac. Sc. Mm. 

(Es.) 30 (*1877) (Suppl.) No. 4, 24 pp. 
fractional expression for (l + Ji) n to any odd 

number of terms. Steggall, J.E.A. Edinb. 

Mth. S. P. 10 (1892) 21-. 
Arithmetic, theorem of Lagrange. Grunert, 

J. A. Arch. Mth. Ps. 47 (1867) 328-. 



77 



1610 



Rational polynomials; divisibility; reducibility 



1610 



Binomials, cube-roots. Homer, W. G. Thom- 
son A. Ph. 8 (1816) 279-, 388-. 

, cubic, x*y 3 . Lame, G. C. E. 61 (1865) 
921-, 961-. 

Common divisors, finding. Buys-Ballot,C.H. D. 
Amst. Vs. Ak. 13 (1862) 430-. 

Condition that/=^0 + J5\t-, where/, A, B, <j>, $ 
are all rational integral polynomials in two 
variables. Halphen, G. H. Par. S. Mth. 
Bll. 5 (1877) 160-. 

Divisibility of (x + y) n + ( - x) n + ( - y) n , Cauchy's 
theorem. Muir, T. [1878] Mess. Mth. 8 
(1879 119-. 

, . Lucas, E. As. Fr. C. E. 

(1888) (Ft. 2) 29-. 

Division, abbreviated algebraic. Reuschle, C. 
Z. Mth. Ps. 41 (1896) 93-. 

, algebraic, applied to homogeneous poly- 
nomials. Andoyer, H. Liouv. J. Mth. 1 
(1895) 61-. 

, , and new theorem of analysis. Le Cointe, 
L. A. N. A. Mth. 1 (1842) 409-. 

of integral polynomials, application to in- 
tegration. Jamet, V. Mars. Fac. Sc. A. 8 
(1898) 151-. 

polynomial by another. Rubini, R. G. 

Mt. 4 (1866) 38-. 
Divisors, algebraic theorem, with application 

to curves. Pasch, M. Crelle J. Mth. 89 

(1880) 252-. 
, commensurable, 2nd degree. Transon, A. 

(Prof.). N. A. Mth. 6 (1847) 305-. 
_, , . Prouhet, E. N. A. Mth. 18 

(1859) 257-. 
given degree of a polynomial. Maleyx, L. 

N. A. Mth. 14 (1875) 97-. 

polynomials with whole numbers for 
coefficients. Perott, J. Par. S. Mth. Bll. 
10 (1882) 250-. 

, rational. Durville, . N. A. Mth. 4 (1845) 

439-. 
, , 2nd degree. Durville, . N. A. Mth. 

4 (1845) 339-. 

of rational polynomials. Bouniakowsky , V. 
[1854] St Pet. Ac. Sc. Mm. 8 (1857) 305-. 

Equations with integral coefficients. Cauchy, 

A. L. C. E. 24 (1847) 407-. 
Expansion of (l+x + x 2 + ...&c.)". Euler, L. 

[1778] St Pet. Ac. Sc. N. Acta 12 (1801) 

47-. 
(l + x + x*) n . Euler, L. [1778] St Pet. 

Ac. Sc. N. Acta 14 (1805) 75-. 
(x + y) n + (-x) n + (-y) n . Muir, T. QJ. 

Mth. 16 (1879) 9-. 
Factorials, class/ Gregory, D. F. Camb. Mth. 

J. 3 (1843) 89-. 

Vandermonde's. Anon, (vi 158) Bb. It. 
(1830) 407-. 

Factorization. Butters, J. W. Edinb. Mth. 

S. P. 12 (1894) 31-; 16 (1898) 78-. 
Factors of integral functions of nth degree. 

Am Ende, . Grunert Arch. 30 (1858) 

442-. 

ax* + bxy +...+/. Grunert, J. A. 
Grunert Arch. 39 (1862) 98-. 

(x + y) n - x n - y n , Cauchy's theorem. 

Glaisher, J. W. L. QJ. Mth. 15 (1878) 365- ; 
16 (1879) 89-. 



Figurate series. Smyth, B. B. Kan. Ac. Sc. 

T. 14 (1896) 29-. 
Formation-law of coefficients in quotient of two 

power series. Jeiek, 0. Prag Sb. (1884) 

(Mth. Nt.) 127-. 
Formula giving x m + y m as function of (x + y) 

and xy. Desboves, A. N. A. Mth. 14 (1875) 

385-. 
H. C. D. Bouverat, . N. A. Mth. 3 (1844) 

329-. 
--- . Cirodde, P. L. N. A. Mth. 4 (1845) 

497-. 
--- of 2 functions of one variable . Trudi , N. 

Nap. Ed. 1 (1862) 153-. 
----- integral functions. Netto, E. 

[1889] Hamb. Mth. Gs. Mt. 2 (1890) (Fest- 

schr. Tl. 2) 36-. 
---- polynomials. Pomey, E. 

N. A. Mth. 7 (1888) 66-, 407-. 
--- and L. C. M. Barrieu, P. (xn) 

Mathesis 3 (1883) 217-. 
--- of 2 polynomials. Craufurd, A.Q. G. 

Camb. Mth. J. 4 (1845) 9-. 

, remainder in the pro- 
cess. Faa de Bruno, F. C. E. 42 (1856) 
407-. 

polynomials, determination by 
determinants. Zeuthen, H. G. (xn) Ts. 
Mth. 5 (1881) 45-, 109-. 

---- 2 rational integral functions of x, 

method. Falk, M. [1878] Ups. S. Sc. N. 

Acta 10 (1879) (No. 11) 5 pp. 
Homogeneous functions, property. Gukovskij, 

A. N. Es. S. Nt. Mm. (Mth.) 11 (1890) 

145-. 
Identities, algebraic class. Glaisher, J. W. L. 

[1878] Mess. Mth. 8 (1879) 53-. 

, , relating to sums of squares. Catalan, 
E. C. Liege S. Sc. Mm. 13 (1886) 33-, 
399. 

, connected with (a + b) n - a* - b n . Sadun, E. 
Ev. Mt. 4 (1894) 189- ; 5 (1895) 19-. 

developed from- = - + ^^.-. Tait,P.G. 

p q q p 

[1877] Edinb. E. S. P. 9 (1878) 416-. 
Identity, algebraic, on differences of 4 letters. 
Glaisher, J. W. L. [1878] Mess. Mth. 8 
(1879) 45-. 

, , reciprocals of cyclic differences. 
Saint-Germain, de. Caen Ac. Mm. (1892) 
(Pt. 1) 15-. 

of polynomials, principle. Roy, A. Mathe- 
matician 3 (1850) 1-. 

-- Waring's, an. Virieu, J. de. N. A. Mth. 
1 (1862) 45-. 

, Waring's analytical proof. Serret, P. N. 
A. Mth. 7 (1848) 199-. 

. Ifa + 6 + c=0, 



(b-c c-a a-b\ 
- + r- + - I 
a b c J 



b 



Glaisher, J. W. L. [1880] Mess. Mth. 10 
(1881) 54-. 

Irreducible factors of x n -l. Kronecker, L. 
Liouv. J. Mth. 19 (1854) 177-. 



78 



1610 Rational polynomials 

Multiplication and division, algebraic. Salim- 

beni, L. Verona Mm. S. It. 7 (1794) 482-. 
Polynomial, complete, number of terms. Ger- 

gonne, J. I). Gergonne A. Mth. 13 (1822-23) 

282-. 
, condition for factor of form x n - a n . Zeipel, 

E. V. von. Ups. N. Acta S. Sc. 4 (1863) 

24pp. 
, . Bjarling, C. F. E. 

Arch. Mth. Ps. 55 (1873) 429-. 
, determination by integrals of its partial 

differentials. Mossbrugger, L. GrunertArch. 

4 (1844) 210-. 
, development, case. Weihrauch, K. Z. 

Mth. Ps. 26 (1881) 127-. 
, without binomial theorem. Brassinne, E. 

Toul. Mm. Ac. 1 (1851) 184-. 

4th degree, values of x for which it is a 
square. Calzolari, L. G. Mt. 7 (1869) 
317-. 

, linear factorisation. Kiipper, K. Casopis 
14 (1885) 28-; Fschr. Mth. (1886) 60. 

, nth power. Studnicka, F. J. Prag Sb. 
(1879) 375-; Casopis 9 (*1880) 49-. 

(x 2 - 1)", property. Polignac, C. de. [1874] 
Par. S. Mth. Bll. 3 (1875) 19-. 

Polynomials, class. Appell, P. Par. EC. Norm. 

A. 9 (1880) 119-. 
, factorisable in linear factors. Moutard, 

. C. E. 119 (1894) 42-. 
, division and extraction of roots. Gergonne, 

J. D. Gergonne A. Mth. 4 (1813-14) 297-. 
, equal factors of . Ostrogradsky, M. A. C.E. 

42 (1856) 930-. 
, geometrical application of theorem. Laisant, 

C. A. As. Fr. C. E. (1898) (Pt. 2) 73-. 
, powers. Brianchon, C. J. Par. EC. Pol. 

J. 15 (1837) (25 cah.) 158-. 
, . Casinelli, A. (s. L.) Bologna N. Cm. 

4 (1840) 453-. 
, . Lewis, W. J. Franklin I. J. 3 (1842) 

44-. 
, , divisibility. Crelle, A. L. Berl. Ab. 

(1839) 1-, 299-. 
, product of two, (Gauss). Terquem, O. N. 

A. Mth. 3 (1844) 47-. 
, properties. De Forest, E. L. Des Moines 

Anal. 7 (1880) 39-, 73-, 105-. 
, , method of demonstrating. De Forest, 

E. L. Des Moines Anal. 10 (1883) 97-. 
, rational factors. Gergonne, J. D. Gergonne 

A. Mth. 12 (1821-22) 309-. 
, , geometric construction. Winckler, A. 

Wien Sb. 53 (1866) (Ab. 2) 326-. 
, roots. Sebuev, G. N. Kazan S. Nt. (Ps.- 

Mth.} P. 7 (1889) 394-. 

of 3rd degree in one variable. Nordlund, 
K. P. Ts. Mt. Fys. 4 (1871) 185-. 

Power of polynomial, expression by symmetric 
functions. Piarron de MondSsir, E. S. As. 
Fr. C. E. (1877) 154-. 

Powers of (a^ + a<& 2 + ) n , theorem. Tralles, 

J. G. Berl. Ab. (1816-17) 56-. 

Principle of greatest and least exponents. Ap- 
plications in theory of algebraic functions. 
Bugaev, N. V. [1889] Eec. Mth. (Moscou) 
14 (1890) 553-. 



Algebraic inequalities 1615 

Quotient and product functions, certain. Guld- 

berg, A. S. Christiania F. (1884) No. 4, 

18pp. 
remainder in (x - l)P/x m . Catalan, E. C. 

Liege S. Sc. Mm. 15 (1888) No. 1, 142-. 
quadrics to sums of squares. Laurent, H. 

N. A. Mth. 19 (1880) 12-; 20 (1881) 38-. 
Series. ~2A n <j>(n)x n . Grunert, J. A. Crelle 

J. 25 (1843) 240- . 
Square root extraction, of 6-nomials, 5-nomials, 

etc. Eeade, J. Thomson A. Ph. 11 (1818) 

31-. 
Sum of a series connected with transvectants. 

Gordan, P. Palermo Cir. Mt. Ed. 12 (1898) 

326-. 
Sums of like powers of (linear) expressions. 

Bierens de Haan, D. N. Arch. Wisk. 5 

(*1879) 208-. 
powers of first n numbers, geometrical 

illustrations. Bochow, K. Magdeb. Nt. Vr. 

Jbr. u. Ab. (1896-98) 165-. 
Ternary forms, conditions for linear factors. 

Brill, A. [1896-98] Mth. A. 50 (1898) 157- ; 

D. Mth. Vr. Jbr. 5 (1901) (Heft 1) 52-. 
Theorems of Bezout and Euler. Poussart, A. 

Ens. Mth. 2 (1900) 136-. 
Transformation of expression 

(la - cy)* + (ex - az) 2 + (ay - bx)*. 

Smith, Arch. Camb. Mth. J. 1 (1839) 

155-. 
(cy - bz) 2 + (az - ex) 2 + (bx - ay) 2 . 

N., M. N. Camb. Mth. J. 2 (1841) 9-. 



E. G. Grunert Arch. 27 (1856) 482-. 
x n + y n expressed in terms of x + y and xy. 
Valeriani, V. G. Mt. 12 (1874) 208-. 

1615 Algebraic inequalities. 

Inequalities, applications. Brashmann, N. D. 

(xn) Mosc. Un. Mm. 10 (1835) 381-. 
, calculus. Fourier, J. B. J. Par. S. Phlm. 

N. Bll. (1826) 99-. 
, . Gergonne, J. D. Gergonne A. Mth. 

17 (1826-27) 134-. 
, extension of theorem in. Rogers, L. J. 

Mess. Mth. 17 (1888) 145-. 
, generalisation of formula of Tschebyscheff 

(Cebysev). Jensen, . Bll. Sc. Mth. 12 

(1888) 134-. 
, means, and imaginaries. Grunert, J. A. 

Grunert Arch. 1 (1841) 268-. 
, note on some, and their application to in- 
tegral calculus. La Vallee-Poussin, C. de. 

Brux. S. Sc. A. 16 (1892) (Pt. 1) 8-. 
, notes. Face, F. C. Mess. Mth. 18 (1889) 

90-. 
, number of conditions expressed by. Sludskil, 

T. A. (xn) [1873] Eec. Mth. (Moscou) 7 

(1874-75) (Pt. 1) 419-. 
, problem. (x m + y m > or < z m when 

x y + y 2 = z' 2 ). Grunert, J. A. Grunert Arch. 

20 (1853) 356-. 



79 



1620 Permutations, combinations, etc. Binomial coefficients 1620 



Inequalities, theorem. Glaisher, J. W. L. 
Mess. Mth. 8 (1879) 140-. 

of Tschebyscheff's (Cebysev), proof. Markov, 
A. A. (xn) Kharkov Mth. S. Com. (1883) 
105- ; Fschr. Mth. (1885) 168, 171. 

{(n-l)Sa 2 >2Sa&}. Grunert, J. A. Grunert 
Arch. 26 (1856) 105-. 

ma m ~ l >^ -j-->mb m - 1 , proof and applica- 
tions. Fort, 0. Schlomilch Z. 7 (1862) 
46-. 

Inequality concerning sums of products of 
numbers. Schiappa Monteiro, A. [1900] 
Lisb. J. Sc. Mth. 6 (1902) 12-. 

, conditions, calculus. Navier, C. L. M. H. 
Par. S. Phlm. Bll. (1825) 66-, 81-. 

, of, Fourier. Cournot, A. A. (\i 
Adds.) Fe"russac Bll. Sc. Mth. 6 (1826) 1-. 

_ a2nf2 " 1 > !Ltl . Walton, W. Mess. Mth. 
a (a 2n - 1) n 
8 (1879) 130-. 

^1^ lies between^ a^and?^. Walker, 
3fl-yl q q y 

G. F. [1882] Mess. Mth. 12 (1883) 37-. 

mx m ~ l (x - 1) ^ x m - 1 > m (x - 1) . Chrystal, 
G. Edinb. Mth. S. P. 6 (1888) 29-. 

, a m b" + b m c n + c m a n > a n b m + b n c m + c n a m . 

Segar, H. W. Mess. Mth. 22 (1893) 47-. 
Mean value. Holder, O. GStt. Nr. (1889) 38-. 

1620 Permutations, combinations, 
partitions, distributions. Bi- 
nomial and multinomial co- 
efficients. 

Algorithms of arithmetical functions. Cesaro, 

E. G. Mt. 23 (1885) 175-. 
Arithmetical cube. Laisant, C. A. As. Fr. 

C. B. (1891) (Ft. 2) 8-. 

tetrahedron. Laisant, C. A. Par. S. Mth. 
Bll. 19 (1891) 18-. 

triangle, history. Fontes, . As. Fr. C. B. 

(1893) (Ft. 2) 236-. 

, properties. Laisant, C. A. As. Fr. 
C. E. (1891) (Ft. 2) 1-; (1893) (Ft. 2) 
206-. 

Arrangement of (1) cards, (2) counters : two 
problems. Crelle, A. L. Crelle J. 44 (1852) 

15 counters in order, generalisation. 
Malmsten, C.^J. Goteb. Hndl. 17 (1882) 77-. 

game (Josephspiel). Curtze, M. Bb. Mth. 

(1894) 116 ; (1895) 34-. 

(Josephus's problem), generalisation. 
Tait, P. G. [1898] Edinb. B. S. P. 22 
(1900) 165-. 

and probabilities, question. Tait, P. G. 
Edinb. B. S. P. 8 (1873) 37-. 

in rows. Brunei, G. Bordeaux S. Sc. PV. 
(1894-95) 28-. 

Arrangements, compound, question in. 

Sylvester, J. J. B. S. P. 12 (1862-63) 

561-. 
, generalisation of theorem of Cauchy. 

Sylvester, J. J. Ph. Mg. 22 (1861) 378-. 



Arrangements, problem. Bouniakmcsky, V. 

[1857] St Pet. Ac. Sc. Bll. 16 (1858) 

67-. 
, . Cayley, A. [1877] Edinb. B. S. P. 

9 (1878) 338-. 
, . Tait, P. G. Edinb. B. S. P. 10 

(1880) 400-. 
, Tait's problem. Muir, T. [1877] Edinb. 

B. S. P. 9 (1878) 382-. 
, . Cayley, A. [1877] Edinb. B. S. 

P. 9 (1878) 388-. 
, . Muir, T. [1881] Edinb. B. S. P. 

11 (1882) 187-. 
of m things of one sort and n things of 

another sort, under conditions of priority. 

Whitworth, W. A. [1878] Mess Mth. 8 

(1879) 105-. 
Binomial' 'calculus." Walsh, J. TillochPh. 

Mg. 63 (1824) 443-. 



BINOMIAL COEFFICIENTS. 

Euler, L. [1778] St Pet. Ac. Sc. N. Acta 

15 (1806) 33-. 
Stockier, F. de B. G. Lisb. Mm. Ac. Sc. 2 

(1799) 480-. 

Pessuti, G. Mod. S. It. Mm. 11 (1804) 446-. 
Mazio, N. G. Arcad. 22 (1824) 27-. 
Arndt, F. Grunert Arch. 3 (1843) 256-. 
Horta, F. Lisb. A. 2 (1858) 98-. 
Le Tauniac, A. N. A. Mth. 20 (1861) 147-. 
Lucas, E. N. A. Mth. 9 (1870) 308-. 
Schlegel, S. F. V. Z. Mth. Ps. 23 (1878) 263-. 
analytic faculties. Trudi, N. [1873] Nap. 

Ac. At. 6 (1875) No. 3, 16 pp. 
Euler's theorem. Wolfers, J. P. Arch. Mth. 

Ps. 45 (1866) 411-. 

formulae. Tardy, P. G. Mt. 3 (1865) 1-. 
. Delannoy, H. As. Fr. C. B. (1890) 

(Ft. 2) 35-. 
a function of, and a series. Siacci, F. G. 

Mt. 10 (1872) 349-. 
and their interpolation. Euler, L. St Pet. 

Ac. Sc. Mm. 9 (1824) 57-. 
note. Busche, E. [1899] Hamb. Mth. Gs. 

Mt. 3 (1900) 379-. 
properties. Schlomilch, 0. Grunert Arch. 1 

(1841) 431- ; 2 (1842) 434-. 
. Tirelli, F. G. Mt. 14 (1876) 318-. 
, and application to combinations. Baur, 

C. W. Z. Mth. Ps. 32 (1887) 218-. 
derived from complex numbers. Studnicka, 

F. J. Prag Sb. (1877) 92-. 
property. Zdrahal, A. Casopis 11 (*1882) 

47-; Fschr. Mth. (*1882) 190. 
. Ekama, H. N. Arch. Wisk. 19 (1892) 

105- ; Fschr. Mth. (1892) 156. 
in relation to gamma function and figurate 

numbers. Matthiessen, . D. Nf. Tbl. 

(*1868) 128- . 
sum of series involving. Bonolis, A. G. Mt. 

11 (1873) 233-. 

n (n-l)(n-2) , . ,, 
1 - + V gg ~ etc> derlved from 

expansion for cos nix. Schlomilch, 0. 
Grunert Arch. 7 (1846) 46-. 



80 



1620 Binomial Coefficients 

sum of squares. Szily, K. Mth. Termt. Ets. 

11 (1893) 330- ; Mth. Nt. B. Ung. 12 (1895) 

84-. 
by Taylor's series. Crelle, A. L. Berl. Ab. 

(1843) 1-. 
theorem. Graves, C. [1865] Ir. Ac. P. 9 

(1867) 297-. 

. Hermes, J. Arch. Mth. Ps. 8 (1890) 269-. 
theorems. Catalan, E. C. Liege S. Sc. Mm. 

15 (1888) No. 1, 41-, 133-, 250-. 
transformation of integral powers into. Trudi, 

N. [1873] Nap. Ac. At. 6 (1875) A T o. 4, 13 pp. 



Binomial theorem, alternative proof. Schuster, 

A. Metz Ac. Mm. 72 (1893) 163-. 
, case. Catalan, E. Brux. Ac. Bll. 16 

(1888) 194. 
, new form. Mendizdbal Tamborrel, J. de. 

Mex. S. "Alzate" Mm. 4 (1890) 117- ; Fschr. 

Mth. (1890) 256. 
before Newton. Marre, A. N. A. Mth. 

5 (1846) 488-. 

for positive integral index. Bouvier, 
L. C. Gergonne A. Mth. 14 (1823-24) 205-. 

. Garcet, . N. A. Mth. 19 

(1860) 32-. 
as case of a general theorem. 

Grunert, J. A. Grunert Arch. 1 (1841) 67-. 
, proofs. Woodcock, T. B. A. Ep. (1889) 

501-. 
, property. Andre, H. d\ N. A. Mth. 5 

(1846) 121-. 
Binomials. Hello, M. P. de. Lisb. Ac. Sc. 

Mm. (Cor.) 4 (Pte. 1) (1815) 41-. 
Card dealing problem, Gergonne's. Dickson, 

L. E. N. Y. Am. Mth. S. Bll. 1 (1895) 

184-. 

game, question. Le Cointe, J. L. A. (vni) 
A. Mt. 5 (1863) 108-. 

games of patience. Badoureau, A. [1881] 
Bv. Sc. 2 (1882) 475-. 

, problem. Vachette, A. N. A. Mth. 5 

(1846) 394-. 

, (i.e. playing cards) and remark on 
theory of substitutions. Petersen, J. P. C. 
(xn) Ts. Mth. 1 (1871) 74-. 

trick. Gergonne, J. D. Gergonne A. Mth. 
4 (1813-14) 276-. 

puzzle and a law of numbers. Steen, A. 
(xn) Ts. Mth. 1 (1865) 49-; 2 (1866) 1-; 
3 (1867) 1-; 6 (1870) 1-, 181- ; 3 (1873) 156-. 

. Hertzsprung, S. (xn) 

Ts. Mth. 3 (1867) 97-. 

. Lorenz, L. V. (xn) 

Ts. Mth. 1 (1871) 53-. 
Cards. Theory of whist. Badoureau, . Ev. 

Sc. 36 (1885) 587-. 



Chess. 

Bishop's move. Cherriman, J. B. (xn) Cn. 
E. S. P. & T. 1 (1883) (Sect. 3) 19. 

Chessboard geometry, and indeterminate equa- 
tion ax + by c. Laquiere, E. M. Par. S. 
Mth. Bll. 7 (1879) 85-. 

, theorem on polygons having vertices at 

VOL. I. 



Chess 1620 

centres of squares. Laisant, C. A. Par. S. 
Mth. Bll. 6 (1878) 156-. 

Chessboard geometry, theorem on triangle 
having vertices at centres of squares. 
Lucas, E. [1877] Par. S. Mth. Bll. 6 
(1878) 9-. 

problem. Lavernede, T. Gard Mm. Ac. 
(1838-39) 151-. 

. "Entre chiens et loup." Lucas, E. 

Ev. Sc. 5 (1883) 555-. 

problems. Lucas, E. Ev. Sc. 17 (1879) 
154- ; 18 (1880) 948-; 19 (1880) 36-, 375-; 
1 (1881) 408-, 783- ; 2 (1882) 365-. 

. Perott, J. Par. S. Mth. Bll. 11 (1883) 

173-. 
End games. Cunningham, (Lt.-Col.) A. B. A. 

Ep. (1894) 564. 
Knight's move. Brewster, (Sir) D. Edinb. Ph. 

J. 9 (1823) 236-. 
. Bouvard, A. Dijon Ac. Mm. (1830) 

23-. 
. Roget, P. M. (vi Adds.) Ph. Mg. 16 

(1840) 305-. 
. Moon, R. Camb. Mth. J. 3 (1843) 

233-. 

. Minding, E. F. A. [1847] St Pet. 
Ac. Sc. Bll. 6 (1848) 209-. 

. Volpicelli, P. C. E. 31 (1850) 314-. 

. Clausen, T. Grunert Arch. 21 (1853) 

91-. 
. Anon, (vi 883) N. A. Mth. 13 (1854) 

181-. 
. Polignac, C. de. C. E. 52 (1861) 

840-. 

. Geynet, A. C. E. 60 (1865) 484. 

. Urusov, (Prince) S. S. (xu) [1865] 

Eec. Mth. (Moscou) 2 (1867) (Pt. 1) 189-. 
_ _. Regnier, A. Les Mondes 32 (1873) 

507-. 
. F rost t A. H. [1876] QJ. Mth. 14 

(1877) 123-. 
. Flye Sainte-Marie, C. Par. S. Mth. 

Bll. 5 (1877) 144-. 
. Polignac, C. (Prince) de. [1880] Par. 

S. Mth. Bll. 9 (1881) 17-. 

. Lucas, E. Ev. Sc. 6 (1883) 370-. 

. Gilbert, G. K. [1885] Smiths. Misc. 

Col. 33 (1888) Art. 2, 88. (Wash. Ph. S. Bll. 7 

(1885).) 
. Hofmann, F. N. A. Mth. 5 (1886) 

224-. 
. Jordan, C. Palermo Cir. Mt. Ed. 2 

(1888) 59-. 
. Brunei, . Bordeaux S. Sc. Mm. 4 

(1894) liii. 

. Wolf, R. Ziir. Vjschr. 39 (1894) 147-. 

, generalisation of problem. Fitting, F. 

Z. Mth. Ps. 45 (1900) 137-. 

illustrating an electrical problem. 
Brunei, . Bordeaux S. Sc. Mm. 2 (1891) 
xxxiv-. 

, number of reentrant moves in half- 
boards. Laquiere, E. M. [1880] Par. S. 
Mth. Bll. 9 (1881) 11-. 

, regular solutions of Euler's problem. 
Laquiere, E. M. Par. S. Mth. Bll. 8 (1880) 
82-, 132-. 

81 F 



1620 Chess 

Knight's move, solution by geometry of posi- 
tion. Volpicelli, P. Em. At. E. Ac. 25 

(1872) 87-, 364-; 26 (1873) 49-, 241-. 
, (Volpicelli) . Tarry, H. Les Mondes 

28 (1872) 60-. 
moves over squares of 5, 6, 7, 8, and 

extension to higher squares. Frost, A. H. 

QJ. Mth. 14 (1877) 354-. 
Mathematical analysis applied to chess. 

(Brief resume.) Janisch, . St Pet. Ac. 

Sc. Bll. 6 (1863) 473-. 
Problem, solution by aid of numerical functions. 

Bugaev, N. V. (xn) [1878] Eec. Mth. 

(Moscou) 9 (1878-81) (Pt. 1) 355-. 
8 queens problem. Glaisher, J. W. L. Ph. 

Mg. 48 (1874) 457-. 
. Eohn, K. Dresden Isis Sb. (1889) 

(Ab.) 89-. 
. Sprague, T. B. Edinb. Mth. S. P. 

8 (1890) 30- ; 17 (1899) 43-. 
, generalisation. Gunther, S. Arch. 

Mth. Ps. 56 (1874) 281-. 
n queens problem. Parmentier, T. As. Fr. 

C. E. (1883) 197-. 
Sylvester's anallagmatic chess-board pattern. 

Lucas, E. As. Fr. C. E. (1877) 213-. 



Class of numbers arising in certain expansions. 

Ocagne, M. d'. Am. J. Mth. 9 (1887) 353-. 
Classes, division into. Harding, P. J. Mth. 

Gz. No. 6 (1895) 59. 
Coefficients in expansion of (x + y) n . Laisant, 

. As. Fr. C. E. (1888) (Pt. 2) 72-. 

._ f ?fz*Y*. Mathieu, J. J. A. N. 
A. Mth. 2 (1863) 509-. 



COMBINATIONS. 
Kirkman, T. P. (n Adds.) Ph. Mg. 5 (1853) 

Buniakovskij, V. Ja. St. Pet. Ac. Sc. Mm. 

(Es.) 21 (*1872) 261-. 

Mantel, W. N. Arch. Wisk. 11 (1884) 190. 
Thiele, T. N. Kjtfb. Ov. (1895) 415-, xv-. 
application to explanation of Arbogast's method. 

De Morgan, A. Camb. and Dubl. Mth. J. 6 

(1851) 35-. 
of a certain number of successive integers 

having a sum below a given limit, number 

of. Marsano, G. B. G. Mt. 19 (1881) 156- ; 

20 (1882) 249-. 

complete. Levret, . N. A. Mth. 1 (1842) 87-. 
. Melon, A.G. N. A. Mth. 8 (1869) 168-. 
. Niewenglmvski, G. H. N. A. Mth. 13 

(1874) 285-. 
compound. Cayley, A. Manch. Lt. Ph. S. 

P. 16 (1877) 113-. 
Crocchi's theorem (on sums of combinations 

of powers and homogeneous products). 

Sylvester, J. J. (xn) [1882] J. H. Un. 

Cir. [2] (1883) 2. 
( ) proof. 

Franklin, F. (xn) [1882] J. H. Un. Cir. 

[2] (1883) 24. 



Combinations 1620 

of 28 dominoes. Eeiss, M. [1859] A. Mt. 5 

(1871-73) 63-. 
of elements dispersed in a plane. Mantel, . 

As. Fr. C. E. (1883) 171-. 
and factorial numbers, theorems. Catalan, E. 

Brux. Ac. Bll. 25 (1893) 238-, 430-. 
formula. Catalan, E. C. Liouv. J. Mth. 7 

(1842) 511-. 
, new. Studnicka, F. J. Prag Sb. (1879) 

295-. 
formulae. Grand, , & EocJiat, . Gergonne 

A. Mth. 3 (1812-13) 213-. 
for expanding power of binomial. Gergonne, 

J. D. Gergonne A. Mth. 17 (1826-27) 

356-. 
a game of. Brianchon, C. J. Par. EC. Pol. 

Cor. 3 (1814-16) 387-. 
number of given class having a given sum. 

Boschi, P. Bologna Ac. Sc. Mm. 5 (1883) 

805-. 
probabilities and life contingencies. Hardy, 

P. Assur. Mg. 2 (*1852) 151-, 259-. 
problem. Euler, L. [1779] St Pet. Ac. Sc. 

Mm. 3 (1811) 57-. 
. Durrande, J. B. Gergonne A. Mth. 7 

(1816-17) 334-. 
. Catalan, E. C. Liouv. J. Mth. 3 (1838) 

111- ; 5 (1840) 264 ; 6 (1841) 74. 
. Chevillard, A. J. N. A. Mth. 3 (1844) 

537-. 
. Kirkman, T. P. Camb. and Dubl. Mth. 

J. 2 (1847) 191- ; 5 (1850) 255-. 
. Anstice, E. E. Camb. and Dubl. Mth. J. 

7 (1852) 279- ; 8 (1853) 149-. 
. Prouhet, E. N. A. Mth. 12 (1853) 85-. 
. Kelland, P. [1855] Edinb. E. S. T. 21 

(1857) 359-. 
. Polignac, (Prince) C. de. [1868] L. Mth. 

S. P. 2 (1869) 69-. 
. Robertson, A. Edinb. Mth. S. P. 4 (1886) 

78-. 
. Hertzsprung, S. Ts. Mth. 5 (1887) 13- ; 

Fschr. Mth. (1887) 198-. 
. Brunei, . Bordeaux S. Sc. Mm. 5 

(1895) xiv-. 
problems. Encontre, D. Mntp. Eec. Bll. 2 

(1805) 68-. 
. Anon, (vi 538) Gergonne A. Mth. 11 

(1820-21) 165-. 
. Weiss, A. Crelle J. 34 (1847) 255-; 38 

(1849) 107-. 

. Sinram,T. Arch. Mth. Ps. 63 (1879) 445-. 
. Holtze,A. Arch. Mth. Ps. 11 (1892) 284-. 
proof for number of combinations of n things 

taken r at a time. Scott, W. H. Mess. 

Mth. 5 (1876) 18-. 
of theorem. Forstemann, W. A. Crelle J. 

13 (1835) 237-. 
. Crone, C. (xn) Ts. Mth. 1 (1877) 

153-. 
questions in. De Morgan, A. Assur. Mg. 5 

(*1855) 93-. 
regular, and applications. Ai\dre, D. Par. EC. 

Norm. A. 5 (1876) 155-. 
with repetition. Martynowski, J. Liege Mm. 

S. Sc, 16 (1861) 53-. 
. Catalan, E. C. Li^ge Mm. S. Sc. 2 

(1867) 1-. 



82 



1620 Permutations, Combinations, Partitions, Distributions, etc. 1620 

Combinations, continued. 

with repetition. Soufflet, . Les Mondes 17 
(1868) 110- ; 24 (1871) 337-. 

. Motta Pegado, L.'P. da. Lisb. J. Sc. 

Mth. 8 (1880) 1-. 

. Gelin, . Mathesis 6 (1886) 175-. 

in sets having odd and even numbers of in- 
versions. Metzler, W. H. Am, J. Mth. 22 
(1900) 55-. 

simple. Andre, D. N. A. Mth. 10 (1871) 
221-. 

special class. Bouniakowsky, V. [1842] St 
Pet. Ac. Sc. Mm. 5 (1844) 297-i 

kind. Buniakovskij, V. J. [1871] St 
Pet. Ac. Sc. Mm. (Es.) 20 (*1872) (Suppl.) 
No. 2, 71 pp. 

theorem. Whitworth, W. A. [1878] Mess. 

Mth. 8 (1879) 82-. 
. Christie, E. W. D. L. Mth. S. P. 20 

(1889) 119-. 

of H. F. Baker. Gegenbauer, L. Wien Ak. 
Sb. 102 (1893) (Ab. 2 a) 951-. 

theorems. Hessel, J. F. C. Grunert Arch. 7 

(1846) 295-. 
. Kirkman, T. P. (n Adds.) Ph. Mg. 4 

(1852) 209- ; (m) Camb. and Dubl. Mth. J. 

8 (1853) 38-. 

. Andre, D. N. A. Mth. 12 (1873) 84-. 
, new. Oettinger, L. Grunert Arch. 15 

(1850) 241- ; Crelle J. 53 (1857) 322-. 
theory. Baur, C. W. Schlomilch Z. 2 (1857) 

267-. 

. Bie, L. H. N. Ts. Mth. 6 (A) (1895) 81-. 
, and application to theory of numbers. 

Stern, M. A. Crelle J. 21 (1840) 91-, 177-. 
and variations, number and sums. Wasmund, 

C. Grunert Arch. 21 (1853) 228-. 



Combinatory aggregation, analysis. Sylvester, 
J. J. Ph. Mg. 24 (1844) 285-. 

analysis. Jacobi, C. G. J. Crelle J. 22 
(1841) 372-. 

, foundations of new theory. MacMalion, 

(Mai.) P. A. Phil. Trans. (A) 194 (1900 

361-. 
, game of mousetrap. Cayley, A. QJ. 

Mth. 15 (1878) 8-. 
, . Steen, A. QJ. Mth. 15 

(1878) 230-. 
, generalisation of elementary. Traversa, 

N. G. Mt. 35 (1897) 174-. 

) inversion of fundamental idea of 
Hindenburg's. Roth, F. Arch. Mth. Ps. 
70 (1884) 427-; 2 (1885) 82-. 

, Mairan's problem. Cournot, A. A. 
Ferussac Bll. Sc. Mth. 11 (1829) 93-. 

, new method in. MacMahon, (Maj.) 
P. A. Camb. Ph. S. T. 16 (1898) 262-. 

, problem. Spottiswoode, W. Ph. Mg. 3 

(1852) 349-. 
, _. Atl dre, D. Par. S. Mth. Bll. 5 

(1877) 150-. 
, . Ocagne, M. d\ N. A. Mth. 19 

(1880) 44-. 
, , solution. Eamus, C. Crelle J. 11 

(1834) 353-. 



Combinatory analysis, summation formulae of 
Steiner, proof. Gudermann, C. [1829] 
Crelle J. 5 (1830) 402-. 

, theorems. Scherk, H. F. Crelle J. 11 

(1834) 226- ; 20 (1840) 360-. 

formula, applications. Gerbaldi, F. G 
Mt. 18 (1880) 308-. 

numbers, graphic representation. Laisant, 
C. A. As. Fr. C. E. (1893) (Pt. 2) 298-. 

problem. Vachette, A. N. A. Mth. 7 
(1848) 421-. 

. Clausen, T. Grunert Arch. 21 (1853) 

93-. 
. Cantor, M. Schlomilch Z. 2 (1857) 

103-. 
, Steiner. Eeiss, M. [1856] Crelle J. 56 

(1859) 326-. 

, . Brunei, G. Bordeaux S. Sc. PV. 

(1896-97) 37-. 

problems. Thibault, . N. A. Mth. 4 
(1845) 627-. 

, class. Hertzsprung, S. Ts. Mth. 4 

(1886) 154- ; Fschr. Mth. (1887) 198. 

, four. Schroder, E. Z. Mth. Ps. 15 

(1870) 361-. 

products, formulae and coefficients for cal- 
culation. Wasmund, C. Grunert Arch. 34 

(1860) 440-. 

symbol of Euler's, use in analysis. Ter- 
quem, 0. Liouv. J. Mth. 4 (1839) 177-. 

systems, order and class. Prouhet, E. 
Liouv. J. Mth. 1 (1856) 321-. 

theorem. Stern, M. A. Crelle J. Mth. 95 
(1883) 102-. 

of Stern, proof. Terquem, O. Liouv. J. 

Mth. 3 (1838) 556-. 
Compositions of numbers, theory. MacMahon, 

P. A. [1892] Phil. Trans. (A) 184 (1894) 

835. 

Connected elements, notation for and distribu- 
tion. Polignac, C. de. As. Fr. C. E. (1884) 

(Pt. 2) 37-. 

Contact and isolation, a problem in permuta- 
tions. Fortey, H. L. Mth. S. P. 15 (*1883- 

84) 98-. 
Cycle, problem of completing a. Waelsch, E. 

Wien Ak. Sb. 90 (1885) (Ab. 2) 160-. 
Derangements. Eodrigues, O. Liouv. J. Mth. 

4 (1839) 236-. 

. Henry, C. N. A. Mth. 20 (1881) 5-. 
. Musso, G. Ev. Mt. 4 (1894) 109-. 
Dirichlet's function [coefficient of \/& in 

(x + -Jb) n ], Daublebsky von Sterneck, E. 

Mh. Mth. Ps. 7 (1896) 342-. 
Distribution of points on a line. Comstock, 

M. L. Des Moines Anal. 1 (1874) 156-. 
Diversities, number of. Lipschitz, . C. E. 

102 (1886) 602-. 
Double of odd number, partition into two odd 

numbers. Maria, P. C. G. Mt. 4 (1866) 

1-, 65-, 193-. 
Dyads formed with 2 elements. Brunei, G. 

Bordeaux S. Sc. PV. (1897-98) 104-. 
even number of elements. Brunei, G. 

Bordeaux S. Sc. PV. (1894-95) 32-. 
n elements, aggregate. Brunei, G. 

Bordeaux S. Sc. PV. (1895-96) 6-. 



83 



1620 Permutations, Combinations, Partitions, Distributions, etc. 1620 



Enumeration of groups of totitives. Tanner, 
H. W. L. L. Mth. S. P. 27 (1896) 329-. 

Equations, linear, symbolic, solution in con- 
nection with theory of permutations. 
Cauchy, A. L. C. B. 21 (1845) 1123-. 

Factorial functions. Piani,D. [1847] Bologna 
Mm. Ac. Sc. 1 (1850) 511-. 

numeration applied to permutations. Lais- 
ant, C. A. Par. S. Mth. Bll. 16 (1888) 
176-. 

n\fr\ (n-r)\ an integer. Miller, W. H. 
Crelle J. 13 (1835) 257-. 

m(m + l)...(m + n-l). Liouville,J. Liouv. 
J. Mth. 2 (1857) 277-. 

Factorials. Bellavitis, G. A. Sc. Lomb. 

Yen. 4 (1834) 10-. 

. McCulloch, J. F. A. Mth. 4 (1888) 
. 161-. 
, approximate expression for xl Forsyth, 

A. E. B. A. Bp. (1883) 407-. 
, value of n! Liouville, J. Liouv. J. 

Mth. 4 (1839) 317-. 
, when n is large. Serret, J. A. 

C. B. 50 (1860) 662-. 

(faculties). Oettinger, L. Crelle J. 33 
(1846) 1-, 117-, 226-, 329-; 35 (1847) 13-; 
38 (1849) 162-, 216- ; 44 (1852) 26-, 147-. 

and faculties, treatment by limits. Ohm, H. 
Crelle J. 39 (1850) 23-. 

, W. G. Homer's method. Homer, J. [1872] 

QJ. Mth. 12(1873)258-. 
, new method. Nicholson, P. Tilloch Ph. 

Mg. 53 (1819) 412-. 
, theorem. Andre, D. (ix) Par. S. 

Mth. Bll. 1 (1873) 84-. 
, numerical values. Kotel'nikov, P. I. (xn) 

Kazan Un. Mm. ((1848) Bk. 4) 9-. 
, ratios of reciprocal. Cauchy, A. L. C. B. 

17 (1843) 921-, 1159-. 
, theorem. Gomes Teixeira, E. Arch. Mth. 

Ps. 2 (1885) 265-. 
Faculties, geometric, and transformation of 

logs, into definite integrals. Cauchy, A. L. 

C. B. 17 (1843) 779-. 

and powers ; analogy. Ampere, A.M. Ger- 
gonne A. Mth. 15 (1824-25) 369-. 

, quotients of two. Schlomilch, 0. Schlo- 

milch Z. 3 (1858) 322-. 
, remarks on some. Guibert, M. P. A. N. 

A. Mth. 19 (1860) 213-. 
, theorem. Schlomilch, 0. Grunert Arch. 

7 (1846) 331-. 
, theory. Bessel, F. W. Konigsb. Arch. 1 

(1812) 241-.' 
, . Kramp, C. Gergonne A. Mth. 3 (1812- 

13) 1-, 114-, 325-. 
, . Miiller, A. Crelle J. 11 (1834) 

361-. 
Faculty coefficients. Studnicka, F. J. Prag 

Ceske Ak. Fr. Jos. Bz. (Trida 2) 9 (1900) 

Art. 17, 10pp.; Fschr. Mth. (1900) 156-. 
, determination. Schlomilch, 0. Grunert 

Arch. (1848) 445-. 

, relations. Schlomilch, O. Grunert 
Arch. 9 (1847) 333-. 

Fractional coefficients. Barsotti, G. Lucca 
At. Ac. 12 (1843) 411-. 



Game of draughts, problem. Lamarle, E. 
[1852] Brux. Ac. Sc. Mm. 27 (1853) 
47 pp. 

Gordian knot (bar and rings), theory. 
Dassen, C. C. Arg. S. Ci. A. 44 (1897) 
337-. 

jumping frog, arrangement of counters 

on board. Berg, F. J. van den. N. Arch. 

Wisk. 12 (1886) 38-; Fschr. Mth. (1885) 

121. 
loto. Du Hays, . Liouv. J. Mth. 7 

(1842) 192-. 

played with 15 pieces on square board of 16 
holes. Bellavitis, G. Yen. I. At. 6 (1880) 
901-. 

of solitaire. Reiss, M. Crelle J. 54 (1857) 
344-. 

. Hermary, . As. Fr. C. B. (1879) 

284-. 
, as problem of analysis and situation. 

Suremain-de-Missery, A. Dijon Ac. Mm. 

(1841-42) 58-. 
Grouping in games. Andre, D. Par. S. Phlm. 

Bll. 1 (1899) 139- ; 2 (1900) 45-, 77-. 

of instruments for simultaneous telegraphy. 
Zetzsche, E. J. Tel. 15 (1891) 201-, 229-, 
255-. 

problems, analytical treatment. Hoyer, P. 
Mth. A. 50 (1898) 499-. 

Homogeneous products of n things of r dimen- 
sions, proof. Walton, W. [1869] QJ. Mth. 
10 (1870) 219-. 

Hyper-magic arithmetical spaces. Laisant, 
C. A. Par. S. Mth. Bll. 22 (1894) 28-. 

squares, general limitations affecting. 
Roberts, S. [1892] L. Mth. S. P. 24 (1893) 
37-. 

La tour d'Hanoi (problem in permutations). 
Allardice, R. E., & Eraser, A. Y. Edinb. 
Mth. S. P. 2 (1884) 50-. 

Latin squares. Cayley, A. Mess. Mth. 19 
(1890) 135-. 

, Euler's. Maillet, E. As. Fr. C. B. 

(1894) (Pt. 2) 244-. 

Magic cubes in n dimensions, way of represent- 
ing in plane. Schlegel, . Par. S. Mth. 
Bll. 20 (1892) 97-. 

cyclovolute. Nulty, E. [1834-44] Am. Ph. 
S. T. 5 (1837) 205- ; 10 (1853) 17-. 

parallelepipeds. Harmuth, T. [1881] Arch. 
Mth. Ps. 67 (1882) 238-. 

rectangles with odd numbers of sides. 
Harmuth, T. Arch. Mth. Ps. 66 (1881) 
413-. 

Magic squares. 

Moon, R. Camb. Mth. J. 4 (1845) 209-. 
Clausen, T. Grunert Arch. 21 (1853) 97-. 
Gyory, S. (xn) Mag. Ak. Ets. (1856) 77-. 
Thompson, W. H. QJ. Mth. 10 (1870) 186-. 
Drach, S. M. Mess. Mth. 2 (1873) 169-, 187. 
Cayley, A. Mess. Mth. 6 (1877) 168. 
Frisby, E. Wash. Ph. S. Bll. 3 (1880) 143-. 
Marchand, D. Les Mondes 2 (1882) 106-, 

247-. 
Rocquigny, F. [G.] de. Les Mondes 2 (1882) 

163. 



84 



1620 Magic Squares 

Arnoux, G. As. Fr. C. E. (1885) (Pt. 1) 94. 
Schoute, P. H. As. Fr. C. E. (1885) (Pt. 2) 

152-. 

Coccoz, . As. Fr. C. E. (1886) (Pt. 2) 130-. 
Frolow, M. As. Fr. C. E. (1886) (Pt. 2) 

170-. 

Clauss, F. Arch. Mth. Ps. 6 (1888) 424-. 
Berg, F. J. van den. N. Arch. Wisk. 16 (1889) 

1- ; Fschr. Mth. (1889) 203. 
Parmentier, (le gen.) . As. Fr. C. E. (1890) 

(Pt. 2) 88-. 
Coccoz, . As. Fr. C. E. (1892) (Pt. 2) 136-, 

[1213]; (1894) (Pt. 2) 163-, 1219; (1895) 

(Pt. 2) 102-. 

Ball, W. W.R. Mess. Mth. 23 (1894) 65-. 
Iznoskov, I. Kazan S. Ps.-Mth. Bll. 5 (1896) 

(Prot.) 48-. 
algebra. Homer, J. QJ. Mth. 11 (1871) 57-, 

123-, 213-. 
application of group theory. Maillet, E. Toul. 

Ac. Sc. Mm. 6 (1894) 258-. 
with base eight. Coccoz, . As. Fr. C. E. 

(1893) (Pt. 2) 171-, 1079. 
case. Holditch, H. QJ. Mth. 6 (1863) 181-. 

of knight's march. Beverley,W. (viAdds.) 
Ph. Mg. 33 (1848) 101-. 

n? numbers. Monteiro, A. S. G. Teix. 

J. Sc. 3 (1881) 81-. 
and cubes. Frost, A. H. QJ. Mth. 7 (1866) 

92-. 
. Barnard, F. A. P. Wash. Nat. Ac. 

Mm. 4 (Pt. 1) (1888) 209-. 

. Mayor, P. Laus. S. Yd. Bll. 27 
(1892) 243-. 

cubes, etc., theory. Moon, E. Camb. and 

Dubl. Mth. J. 1 (1846) 160-. 
doubly magic. Laquiere, E. M. As. Fr. C. E. 

(1880) 243-. 
etc. Harmuth, T. Arch. Mth. Ps. 66 (1881) 

286-. 
Euler's. Boije af Gennas, C. 0. [1898] 

Stockh. Ak. Hndl. Bh. 24 (Afd. 1) (1899) 

No. 2, 15 pp. 
and Gauss. Gunther, S. Z. Mth. Ps. 21 

(1876) (Suppl.) 61-. 
where highest number is prime, law. Tychsen, 

C. (XH) Ts. Mth. 1 (1865) 55-. 
most perfect forms. McClintock, E. Am. J. 

Mth. 19 (1897) 99-. 
and other such arrangements. Smyth, B. B. 

Kan. Ac. Sc. T. 14 (1896) 46-. 
proof of theorem. G anther, S. Arch. Mth. 

Ps. 57 (1875) 285-. 



Mixtures, problem. Coupy, E. N. A. Mth. 6 
(1847) 14-. 

li'ads formed with n 2 elements. Brunei, G. 
Bordeaux S. Sc. PV. (1894-95) 56-. 

v cycles of 2c + l elements. Brunei, G. Bor- 
deaux S. Sc. PV. (1898-99) 71-. 

Nasik cubes. Frost, A. H. QJ. Mth. 8 (1867) 
74. 

-, general properties. Frost, A. H. [1877] 

QJ. Mth. 15 (1878) 93-, 366-. 

squares of any order, construction. Frost, 
A. H. L. Mth. S. P. 27 (1896) 487-. 



Permutations, etc. 1620 

Nasik squares, general properties. Frost, A. 

H. [1877] QJ. Mth. 15 (1878) 34-. 
Network representing benzene. Brunei, G. 

Bordeaux S. Sc. Mm. 4 (1894) xviii-. 
Notation [a a a 2 . . . a p ] < m) to represent expansion 

of mth power of polynomial ^ + 0,2 + ... + a p . 

Ocagne, M. d'. N. A. Mth. 2 (1883) 220-. 
Number of complete arrangements satisfying 

given conditions. Andre, D. C. E. 87 

(1878) 838-; Par. S. Mth. Bll. 7 (1879) 

43. 
distributions with repetition of given class 

and weight. Caldarera, G. G. Mt. 31 (1893) 

161-. 
partitions of a rational integer into sums. 

Hermes, J. Mth. A. 45 (1894) 371- ; 47 

(1896) 281-. 
permutations of n elements presenting 

sequences. Andre, D. C. E. 97 (1883) 

1356-. 
substitutions falling into given number 

of cycles. Schroder, E. Arch. Mth. Ps. 68 

(1882) 353-. 
ways of getting sum not exceeding n, from 

terms of series 1,2, 3.... Plainer, G. Mil. 

I. Lomb. Ed. 21 (1888) 690-, 702-. 
Numbers, 4m + 2 as sum of 12 squares. 

Liouville, J. Liouv. J. Mth. 5 (1860) 

143-. 
Partition analysis applied to properties of any 

system of consecutive integers. MacMahon, 

(Maj.) P. A. [1899] Camb. Ph. S. T. 18 

(1900) 12-. 



Partition of numbers. 

Warburton, H. [1847] Camb. Ph. S. T. 8 

(1849) 471-. 
Battaglini, G. Nap. Ac. Sc. Mm. 2 (1855-57) 

353-. 
Cayley, A. [1855-57] Phil. Trans. (1856) 

127- ; (1858) 47-; Ph. Mg. 13 (1857) 245-. 
Brioschi, F. Tortolini A. 8 (1857) 5-. 
Sylvester, J. J. QJ. Mth. 1 (1857) 81-, 141-, 

198- ; Tortolini A. 8 (1857) 12-. 
Volpicelli, P. Tortolini A. 8 (1857) 22-. 
Bellavitis, G. Tortolini A. 2 (1859) 137-. 
Lanavicensis, (Pseud.) [J. J. Sylvester'] Ph. 

Mg. 18 (1859) 283-. 
Trudi, N. (xi) Nap. Ac. At. 2 (1865) No. 23, 

50pp. 

Catalan, E. C. N. A. Mth. 8 (1869) 407-. 
Buniakovskij, V. Ja. [1874] St Pet. Ac. Sc. 

Mm. (Rs.) 25 (*1875) (Suppl.) No. 1, 29pp. 
Glaisher, J. W. L. C. E. 80 (1875) 255-. 
Laguerre, E. Par. S. Mth. Bll. 5 (1877) 76-. 
Faa de Bruno, F. C. E. 86 (1878) 1189-, 

1259. 
David, . C. E. 90 (1880) 1344- ; 91 (1880) 

621-. 
Catalan, E. C. Liege S. Sc. Mm. 12 (1885) 

No. 2, 19-, 56-, 264-; 13 (1886) 314-. 
Pomey, J. B. N. A. Mth. 4 (1885) 408-. 
Polignac, C. de. C. E. 104 (1887) 1688-. 
Glosel, K. Mb.. Mth. Ps. 7 (1896) 133-, 290. 
Mathews, G. B. L. Mth. S. P. 28 (1897) 

486-. 



85 



1620 Partition of Numbers 

addition to theory. Csorba, G. Mth. Termt. 

Ets. 17 (1899) 189-. 
application of theorem of Eisenstein. Catalan, 

. As. Fr. C. E. (1886) (Pt. 1) 86. 
certain special. MacMahon, (Capt.) P. A. QJ. 

Mth. 21 (1886) 367-. 
formulae. Pepin, . Liouv. J. Mth. 4 (1888) 

83-. 
graphic proof of theorem of Euler's. Sylvester, 

J. J. C. E. 96 (1883) 1110-. 
whose graphs possess symmetry. MacMahon, 

(Maj.) P. A. [1898] Camb. Ph. S. T. 17 

(1899) 149-. 
number of ways of breaking up a number with 

one law of subordinate partition. Volpicelli, 

P. Em. At. 10 (1856-57) 43-, 122-. 
outlines of seven lectures. Sylvester, J. J. 

L. Mth. S. P. 28 (1897) 33-. 
points of analysis depending on. Trudi, N. 

[1877] Nap. Ac. At. 8 (1879) No. 1, 

88 pp. 
problem. Chrystal, G. Edinb. Mth. S. P. 2 

(1884) 49-. 
and other problems, application of Arbogast's 

method of derivations. David, . Liouv. 

J. Mth. 8 (1882) 61-. 
proof of theorem. Volpicelli, P. C. E. 40 

(1855) 1150-. 
. Zuchristian, J. Mh. Mth. Ps. 4 

(1893) 185-. 
question. Boschi, P. Bologna Ac. Sc. Mm. 1 

(1880) 555-. 
theory. MacMahon, P. A. [1896] Phil. Trans. 

(A) 187 (1897) 619- ; 192 (1899) 351-. 
two theorems. Volpicelli, P. N. A. Mth. 14 

(1855) 314-. 
verification formulae. Glaisher, J. W. L. E. 

S. P. 24 (1876) 250-. 



Partition of pentagonal numbers, graphic proof 

of Euler's theorem. Sylvester, J. J. C. E. 

96 (1883) 743-. 
polygon by diagonals, series for. Binet, 

J. P. M. Liouv. J. Mth. 8 (1843) 394-. 
, problem. Ocagne, M. d'. Par. S. Mth. 

Bll. 28 (1900) 157-. 

-series, note. Cayley, A. Am. J. Mth. 6 
(1884) 63-. 

, solution of problem, and types of abacus. 
MacMahon, (Maj.) P. A. Par. S. Mth. Bll. 
26 (1898) 57-. 

of sum of money, number of ways. 
Schubert, H. C. H. Hamb. Mth. Gs. Mt. 1 
(1889) 269. 

table for binary quantics, specimen. 
Cayley, A. Am. J. Mth. 4 (1881) 248-. 

tables, non-unitary. Cayley, A. Am. J. 
Mth. 7 (1885) 57-. 



PAETITIONS. 

Cayley, A. QJ. Mth. 1 (1857) 183-. 
Franklin, F. Am. J. Mth. 2 (1879) 187- ; (xn) 

J. H. Un. Cir. [2] (1883) 72. 
Ely, G. S. J. H. Un. Cir. [3] (1884) 76-. 



Partitions 1620 

Barcroft, D. J. H. Un. Cir. [5] (1885-86) 

64. 
algebraic expression. Herschel, (Sir) J. F. W. 

Phil. Trans. (1850) 399-. 
theorems connected with theory. Forsyth, 

A. R. [1895] L. Mth. S. P. 27 (1896) 

18-. 
of complex numbers (theorem contained in 

theorem of Jacobi's). Sylvester, J. J. C. B. 

96 (1883) 1276-. 
compound, general theory. Sylvester, J. J. 

Ph. Mg. 16 (1858) 371-. 
, method of graphs applied to. Ely, G. S. 

Am. J. Mth. 6 (1884) 382-. 
constructive theory. Sylvester, J. J. Am. J. 

Mth. 5 (1882) 251- ; 6 (1884) 334-. 
, Sylvester's. Jenkins, M. Am. J. Mth. 

7 (1885) 74-. 
and derivations. Glaisher, J. W. L. B. A. 

Ep. (1874) (Sect.) 11-. 

double. Cayley, A. Ph. Mg. 20 (1860) 337-. 
formulae of verification. Glaisher, J. W. L. 

B. A. Ep. (1875) (Sect.) 11-. 
fundamental theorem. Sylvester, J. J. (xn) 

[1882] J. H. Un. Cir. [2] (1883) 22. 
graphical method. Sylvester, J. J. (xii) J. 

H. Un. Cir. [2] (1883) 70-. 
isomerism, graphical representation. Brunei, 

G. Bordeaux S. Sc. PV. (1898-99) 108-. 
, problem (to find number of compounds 

that can be formed by n m-valent atoms and 

(ra - 2) n + 2 univalent atoms) . Franklin, F. 

Am. J. Mth. 1 (1878) 365-. 
miscellaneous theorems. Glaisher, J. W. L. 

Mess. Mth. 5 (1876) 164-. 
of non-pentagonal number. Jacobi, C. G. J. 

Crelle J. 32 (1846) 164-. 
note. Glaisher, J. W. L. Ph. Mg. 49 (1875) 

307-. 
. Mitchell, 0. H. (xn) J. H. Un. Cir. [1] 

(1882) 210. 
. Ely, G. S. (xn) J. H. Un. Cir. [1] 

(1882) 211. 
of a polygon. Cayley, A. L. Mth. S. P. 22 

(1891) 237-. 
problem. Cayley, A. Mess. Mth. 7 (1878) 

187-. 
. Brunei, <?. Bordeaux S. Sc. PV. (1894- 

95) 24-. 
, note. Tail, P. G. Edinb. E. S. T. 32 

(1887) 340-. 
and theory of forms. Capelli, A. [1880] 

G. Mt. 19 (1881) 87-. 
product 1 - x . 1 - x 2 . 1 - x 3 , Franklin's theory. 

Cayley, A. (xn) J. H. Un. Cir. [2] (1883) 

86. 
proof of Sylvester's theorem. Roberts, S. QJ. 

Mth. 4 (1861) 155-. 
theorem. Jenkins, M. Am. J. Mth. 

6 (1884) 331-. 
question. Sylvester, J. J. (xn) J. H. Un. 

Cir. [1] (1882) 179. 
of R and of the .R-gon. Kirkman, T. P. 

Manch. Lt. Ph. S. Mm. & P. 7 (1893) 211- ; 

8 (1894) 109-. 
r-, of r 2 -r + l. Kirkman, T. P. Lane. T. 

Hist. S. 9 (1857) 127-. 



86 



1620 Permutations, etc. 

Partitions, continued. 

7-, of X. Xirkman, T. P. Manch. Ph. S. Mm. 

14 (1857) 137-. 
self -opposite, number of. Durfee, W. P. (xn) 

[1882J J. H. Un. Cir. [2] (1883) 23. 
, (Durfee). Sylvester, J. J. (xn) 

J. H. Un. Cir. [2] (1883) 23-, 42-. 
theorem. Glaisher, J. W. L. [1879-83] Mess. 

Mth. 9 (1880) 47-; 12 (1883) 158-. 
. Sylvester, J. J. C. E. 96 (1883) 674^. 
, new. Sylvester, J. J. (xn) J. H. Un. 

Cir. [2] (1883) 70. 
theorems. Mansion, P. Mess. Mth. 5 (1876) 

90. 
. Glaisher, J. W. L. Mess. Mth. 5 (1876) 

91. 
theory, note. Sylvester, J. J. B. A. Ep. 41 

(1871) (Sect.) 23-. 



Perfect partitions of numbers and compositions 
of multipartite numbers. Macmahon, (Major) 
P. A. Mess. Mth. 20 (1891) 103-. 

Permutants, theory. Cayley, A. Camb. and 
Dubl. Mth. J. 7 (1852) 40-, 97-. 

Permutation, alternate, probability of. Andre, 
D. C. E. 97 (1883) 983-. 

, geometrical. Cayley, A. Ph. Mg. 30 
(1865) 370-. 

numbers, approximate calculation. Schlo- 
rnilch, 0. Z. Mth. Ps. 10 (1865) 232-. 



PEEMUTATIONS. 

Conti, C. Padova N. Sag. 3 (1831) 90-. 
Cayley, A. Ph. Mg. 34 (1849) 527-. 
Bourget, J. N. A. Mth. 10 (1871) 254-. 
Lucas, E. As. Fr. C. E. (1883) 83-. 
alternate. Andre, D. Liouv. J. Mth. 7 (1881) 
167-. 

and quasi-alternate, relation between num- 
ber of. Andre, D. Par. S. Phlm. Bll. 8 
(1896) 5-. 

application of new method to. Sprague, T. B. 

Edinb. E. S. T. 37 (1895) 399-. 
a certain species. Andre, D. Par. S. Phlm. 

Mm. Cent. (1888) 35-. 
circular, applications to theory of numbers. 

MacMahon, (Maj.) P. A. L. Mth. S. P. 23 

(1892) 305-. 

distinct. Moreau, C. N. A. Mth. 11 (1872) 
309-. 

, notion of maxima and minima in. Andre, 

D. Par. S. Phlm. Bll. 5 (1893) (C. E. No. 11) 

2-. 
, sequences. Andre, D. Par. S. Mth. Bll. 

23 (1895) 122-. 
and combinations. Pagnini, G. M. Brugna- 

telli G. 3 (1810) 329-. 
. Warburton, H. [1847] Camb. Ph. S. 

T. 8 (1849) 471-. 
. Whitworth, W. A. [1865] Mess. Mth. 

3 (1866) 193-. 
, problem. Balbo, P. Turin Mm. Ac. 14 

(1804-5) 224-. 



Permutations 1620 

and combinations, proofs of theorems, and of 
theorem in stereometry. Seidelin, C. J. L. 
(xn) Ts. Mth. 6 (1870) 20-, 22-; 6 (1876) 
63-. 

, theory. Hertzsprung, S. (xn) Ts. 
Mth. 5 (1869) 97-. 

continuous, by uniform law. Paradisi, G. 
[1816] Mod. Mm. S. It. 18 (1818) 143-. 

and cyclic arrangements, theory. Jablonski, E. 
C. E. 114 (1892) 904- ; Liouv. J. Mth. 8 
(1892) 331- ; Prace Mt.-Fiz. 4 (1893) 

of first n integers, method of deducing con- 
secutively. Renshaw, A. Mess. Mth. 4 
(1868) 36-. 

numbers, distribution into 4 groups. 

Andre, D. Par. S. Phlm. Bll. 5 (1893) 
33-. 

n letters, classification in groups. Despeyrous, 
C. Liouv. J. Mth. 10 (1865) 177-. 

2q letters alike in pairs. Vachette, A. N. 
A. Mth. 13 (1874) 549-; 14 (1875) 299-, 
337-. 

3q letters alike in threes. Vachette, A. N. 
A. Mth. 14 (1875) 438-. 

. Moreau, C. N. A. Mth. 15 

(1876) 90-. 
. Vachette, A. N. A. Mth. 15 

(1876) 114-, 145-, 193-. 
limited. Laisant, C. A. C. E. 112 (1891) 

1047-. 
maxima, minima and sequences. Andre, D. 

Par. EC. Norm. A. 1 (1884) 121-. 
new calculus, applicable to theory. Cauchy, 

A. L. C. E. 22 (1846) 53-, 99-. 

demonstration of theorem. Andre, D. Par. 
S. Phlm. Bll. 3 (1891) 153-. 

notes. Morley, F. N. Y. Mth. S. Bll. 3 (1894) 

142-. 
of a number, sum. Marre, A. N. A. Mth. 5 

(1846) 57-. 

n objects. Bourget, J. N. A. Mth. 2 (1883) 
433-. 

problem. Barlow, P. Nicholson J. 23 (1809) 

203-. 
. Arndt, F. Grunert Arch. 3 (1843) 

210-. 
. Allardice, R. E. Edinb. Mth. S. P. 8 

(1890) 64-. 

. Lagrandval, de. Bordeaux S. Sc. PV. 

(1895-96) 22-. 
, solution. Drot, . N. A. Mth. 5 (1846) 

97-. 
problems, two. Laisant, . Par. S. Mth. Bll. 

19 (1891) 105-. 
quasi-alternate. Andre, D. C. E. 119 (1894) 

947-; Liouv. J. Mth. 1 (1895) 315-. 
with restrictions as to placing. Kantor, S. 

Z. Mth. Ps. 28 (1883) 379-. 
Schubert's solution of Bachet's problem. 

Busche, E. Mth. A. 47 (1896) 105-. 
self -con jugate. Muir, T. Edinb. E. S. P. 17 

(1891) 7-. 

. MacMahon, (Maj.) P. A. Mess. Mth. 24 

(1895) 69-. 
with sequences. Morley, F. [1897] N. Y. Am. 

Mth. S. Bll. 4 (1898) 23-. 



Permutations, continued. 

square, of base 6. Tarry, G. Liege S. Sc. 

Mm. 2 (1900) No. 1, 10 pp. 
successive, problem of Monge's. Bourget, J. 

Liouv. J. Mth. 8 (1882) 413-. 
theorem of MacMahon's. Gegetibauer, L. Mb.. 

Mth. Ps. 11 (1900) 287-. 
theory. Despeyrous, C. Liouv. J. Mth. 6 

(1861) 417-. 
transformation and classification. Sprague, 

T. B. Edinb. Mth. S. P. 9 (1891) 59-. 



1620 Permutations, Combinations, Partitions, Distributions, etc. 1620 

Sum of numbers of all variations p + 1, p + 2 . . . 
to ?d;h class inclusive =n (n- 1) ... (n-p- 1) 
{[e(n-p) !]-!} Huber,M.T. Wiad. Mt. 
3 (1899) 39-; 4 (1900) 93; Fschr. Mth. 
(1899) 208. 

Symmetric functions of numbers, and their 
partition. Scott, G. [1865] QJ. Mth. 7 
(1866) 81-. 

Tactic disclosing existence of 4-valued func- 
tions. Sylvester, J. J. Ph. Mg. 21 (1861) 
515- ; 22 (1861) 45-. 
of 9 elements. Sylvester, J. J. Ph. Mg. 22 

(1861) 144-. 
Tactical memoranda. Moore, E. H. Am. J. 

Mth. 18 (1896) 265-. 
Ternary systems of 13 elements. Pasquale, V. 

de. Mil. I. Lomb. Ed. 32 (1899) 213-. 
Thirty cubes constructed with six differently 
coloured squares. MacMahon, (Maj.) P. A. 
L. Mth. S. P. 24 (1893) 145-. 
Thirty-six officers, problem. Tarry, G. As. 

Fr. C. K. (1900) (Ft. 2) 170-. 
'Trees.' Cayley,A. Ph. Mg. 13 (1857) 172- ; 

18 (1859) 374-. 
. Polignac, C. de. Par. S. Mth. Bll. 8 

(1880) 120- ; 9 (1881) 30-. 
. Cayley, A. (xn) J. H. Un. Cir. [1] 

(1882) 202. 
. Sylvester, J. J. (xn) J. H. Un. Cir. [1] 

(1882) 202-. 

, with application to theory of chemical com- 
binations. Cayley, A. B. A. Ep. (1875) 
257-; Am. J. Mth. 4 (1881) 266-. 

, . Delannoy, H. As. 

Fr. C. E. (1894) (Pt. 2) 102-. 
, isomers, theory. Cayley, A. Ph. Mg. 47 

(1874) 444-. 
, number of univalent radicals C,,!!^,,. 

Cayley, A. [1876] Ph. Mg. 3 (1877) 34-. 
, theorem. Cayley, A. QJ. Mth. 23 (1889) 

376. 

, yoke-chains and multipartite compositions 
in connexion with. MacMahon, (Maj.) P. A. 
L. Mth. S. P. 22 (1891) 330-. 
Triads. Fifteen girl problem. Kirkman, T. P. 
Ph. Mg. 37 (1850) 169; 23 (1862) 199-. 

. (Kirkman). Woolhouse, W. S. B. 

Ph. Mg. 22 (1861) 510- . 

. . Cayley, A. Ph. Mg. 25 (1863) 59-. 

. . Power, J. [1865] QJ. Mth. 8 

(1867) 236-. 

. . Frost, A. H. QJ. Mth. 11 

(1871) 26-. 

. . Johnson, W. W. Am. J. Mth. 

2 (1879) 397-. 

. . Story, W. E. Am. J. Mth. 2 

(1879) 399-. 
. . Mertelsmann, A. F. H. Z. 

Mth. Ps. 43 (1898) 329-. 
. , cyclic solution. Peirce, B. 
Gould As. J. 6 (1861) 169-. 

. , geometric picture of. Davis, 

E. W. A. Mth. 11 (1896-97) 156-. 

. ,3 methods and 48 solutions. 

Frazer, P. (jun,). Am. Ph. S. P. 18 (1880) 
505-. 

. , note on theory. Tait, P. G. 

Edinb. E. S. P. 10 (1880) 664-. 



Polygons, division into triangles. (Segner's 

numbers.) Lame, G. Liouv. J. Mth. 3 

(1838) 505-. 
, . ( .) Tellkampf, A. Grunert 

Arch. 2 (1842) 117-. 
, . ( .) Catalan, E. C. 

[1870] Liege S. Sc. Mm. 13 (1886) 54-, 

399. 
, . ( .) Rowe, E. C., & Taylor, 

H. M. L. Mth. S. P. 13 (1881-82) 102-. 
, . ( .) Gelin, (I'abbe) E. (xn) 

Mathesis 3 (1883) 108-. 
, . ( .) Catalan, E. C. [1886] 

Palermo Cir. Mt. Ed. 1 (1887) 190-. 
Polynomial coefficients. Piuma, C. M. G. Mt. 

29 (1891) 34-. 
. Klekler, P. Mh. Mth. Ps. 10 (1899) 

218-. 
, properties. Sadun, E. G. Mt. 31 (1893) 

119-, 379. 
theorem. Ladd, C. Des Moines Anal. 5 

(1878) 145-. 
Products of n factors, number of. Eodrigues, 0. 

Liouv. J. Mth. 3 (1838) 549. 
Quadricycles of 8;i + l elements, construction. 

Brunei, G. Bordeaux S. Sc. PV. (1895-96) 

58-. 

n elements, systems. Brunei, G. Bor- 
deaux S. Sc. PV. (1898-99) 59-. 
" Quotites " of combinations. Soule, . Bor- 
deaux S. Sc. Mm. 3 (1893) xiv-, xxv-. 
Series for n ! . Heather, J. F. Mathematician 

2 (1847) 296-. 



properties and application. Unferdinger, F. 
Wien Sb. 67 j(1873) (Ab. 2) 363-. 

7l w 

2 : for -i = l,2, 3, 4, 5, summation. Dobin- 

ski, G. Arch. Mth. Ps. 61 (1877) 333-. 
Signs, successions of, and application to 

coloured tiles and Newton's rule, etc. 

Sylvester, J. J. Ph. Mg. 34 (1867) 461-. 
Stifel's bordered squares. Fontes, . As. Fr. 

C. E. (1895) (Pt. 2) 248-. 
Sub-factorial N. Whitworth, W. A. Mess. 

Mth. 7 (1878) 145-. 
Sum of the cubes of the coefficients in (1 - z) 2 ". 

Richmond, H. W. Mess. Mth. 21 (1892) 

77-. 



1625 Finite Summation 

Triads. Fifteen girl problem, solution. Carp- 
mael, E. L. Mth. S. P. 12 (1880-81) 148-. 

formed with 6 + l elements, systems. 
Brunei, G. As. Fr. C. E. (1895) (Pt. 2) 
145. 

6n - 1 and 6w - 2 elements. Brunei, 

G. Bordeaux S. Sc. PV. (1895-96) 40-. 

. Nine girl problem. Sylvester, J. J . Mess. 
Mth. 22 (1893) 159-, 192. 

of once-paired elements. Homer, J. [1867] 
QJ. Mth. 9 (1868) 15-. 

-7 and 15 things. Cayley, A. Ph. Mg. 

37 (1850) 50-. 
Triangle of sequences. Andre, D. C. B. 118 

(1894) 575-, 726. 
Vandermonde's theorem. Collins, E. [1839] 

St Pet. Ac. Sc. Bll. 6 (1840) 81-. 
. Tanner, H. W. L. Mess. Mth. 25 (1896) 

, generalisation. Hill, M. J. M. Mess. 

Mth. 25 (1896) 154-. 
Various theorems. Clausen, T. Crelle J. 4 

(1829) 278-. 
Voting. Macfarlane, A. Edinb. Mth. S. P. 2 

(1884) 25-. 



1625 Finite Summation. Recur- 
ring 1 series. 

Arithmetical formula. Netto, E. Mth. A. 49 
(1897) 148. 

series. San Bertolo, N. Em. At. 10 (1856- 
57) 78-. 

. Jung, V. Casopis 28 (1899) 281- ; 
Fschr. Mth. (1899) 244. 

of different orders. Jarolimek, C. 6a- 

sopis 6 (*1877) 91-; Fschr. Mth. (*1877) 

176. 
, sum of cubes of terms. Shidy, L. P. 

Des Moines Anal. 3 (1876) 51-. 
, whose ultimate differences are constant. 

Pollock, (Sir) F. [1850] E. S. P. 5 (1851) 

852-. 
Binomial expansion, summation of terms. 

Querret, . Gergonne A. Mth. 15 (1824-25) 

189-. 
Combination sums of squares of even and odd 

numbers, relations. Oppolzer, T. von. Mth. 

A. 13 (1878) 405-. 
Combinatory numbers, certain. Lemeray, . 

As. Fr. C. E. (1899) (Pt. 2) 99-. 

Continued product II (1 + i.c), expansion in 

i=0 

powers of x, coefficients. Schlafii, L. C. E. 
25 (1847) 381- ; Grunert Arch. 10 (1847) 
386-; 12 (1849) 53-; Crelle J. 43 (1852) 

Equations generating recurring series. Andre, 

D. Par. S. Mth. Bll. 6 (1878) 166-. 
Expansion in recurring series, extension, and 

physical application. Topler, A. Steierm. 

Mt. (1872) 64-. 
Factorial expression, summation. Cayley, A. 

Ph. Mg. 13 (1857) 419-. 



Figurate Numbers 1625 

Factorial expressions, transformations. Plarr, 

G. B. A. Ep. (1857) 101-. 
Factorials, formula involving. Ellis, J. C. W. 

QJ. Mth. 8 (1867) 256-. 



Figurate numbers. 

Barruel, E. Par. EC. Pol. Cor. 2 (1809-13) 

220-. 
Gergonne, J. D. Gergonne A. Mth. 4 (1813-14) 

115. 

Brassinne, E. N. A. Mth. 6 (1847) 120-. 
Transon, A. (Prof.). N. A. Mth. 9 (1850) 255-. 
Nicolaides, N. Les Mondes 7 (1865) 693-; 8 

(1865) 615-, 708-. 
Le Cointe, J. L. A. Les Mondes 8 (1865) 

707-. 

Soufflet, . Les Mondes 13 (1867) 336-. 
Hochheim, A. Arch. Mth. Ps. 55 (1873) 

189-. 
formulae, proofs. Stegmann, F. Grunert Arch. 

5 (1844) 82-. 
new method. Nicholson, P. Tilloch Ph. Mg. 

53 (1819) 412-. 
polygonal numbers. Gough, J. Nicholson J. 

20 (1808) 161-. 
. Barlow, P. Nicholson J. 21 (1808) 

118-. 
. Gough, J. Nicholson J. 21 (1808) 

241-. 
. Barlow, P. Nicholson J. 22 (1809) 

33. 

. Musso, G. G. Mt. 31 (1893) 173-. 

. Catalan, E. G. Mt. 31 (1893) 227-. 

. Berger, A. Ups. S. Sc. N. Acta 17 

(1898) No. 4, 38 pp. 
, Fermat's theorem. Pollock, (Sir) F. 

Phil. Trans. (1861) 409- ; E. S. P. 13 (1864) 

542-. 
, . Pepin, T. Em. N. Line. At. 46 

(1893) 119-. 
, , extension. Pollock, (Sir) F. 

[1850] E. S. P. 5 (1851) 922-. 
, , . Maillet, E. Par. S. Mth. 

Bll. 23 (1895) 40-; Liouv. J. Mth. 2 (1896) 

363-. 
, , general proof. Cauchy, A.L. Par. 

Mm. de PL (1813-15) 177-. 
, formula for. Laisant, C. A. Par. S. 

Phlm. Bll. 3 (1891) 29-. 
polyhedral numbers. Giudice, . Palermo 

Cir. Mt. Ed. 3 (1889) 231. 
sums. Brassinne, E, N. A. Mth. 6 (1847) 

120-. 
theorem. Bjorling, E. G. Grunert Arch. 7 

(1846) 266-. 

triangular numbers. Casinelli, A. (s. L.) Bo- 
logna N. Cm. 2 (1836) 415-. 
, summation of like powers of first n. 

Barbette, E. Mathesis 15 (1895) 111-. 
, theorems. Liouville, J. Liouv. J. Mth. 

7 (1862) 407- ; 8 (1863) 73-. 
, . Glaister, J. W. L. Mess. Mth. 5 

(1876) 164-. 
trigonal numbers. Stern, M. A. Crelle J. 69 

(1868) 370-. 



89 



1625 



Finite Summation. Recurring Series 



Finite series. Verniory, . Mathesis 12 
(1892) 217-. 

, extension by arbitrary parameters. 
Most, R. Arch. Mth. Ps. 48 (1868) 104-. 

-- , sum. Stern, M. A, Crelle J. 33 (1846) 
362. 

, summation. Lindman, C. F, Stockh. 
Ofv. 17 (1860) 415- ; Grunert Arch. 38 (1862) 
246-. 

-- , , and application to sin n a; and cos" a;. 

Simony, O. Arch. Mth. Ps. 55 (1873) 64-. 
Integral power of integer representable as sum 

of consecutive odd numbers. Studnicka, 

F. J. Casopis 13 (1884) 30- ; Fschr. Mth. 

(1884) 212. 
Multinomial coefficients, sum of all. Jones, S. 

Thomson A. Ph. 4 (1822) 27-. 
-- , summation. Masters, W. Beng. As. S. 

J. 1 (1832) 187-. 
Numbers, theorem 2r 3 = (2r) 2 , generalisation. 

Liouville, J. Liouv. J. Mth. 2 (1857) 393-. 
Piles of shot. Eoche, . Quetelet Cor. Mth. 

6 (1830) 199-. 

--- . Guilmin, A. N. A. Mth. 3 (1844) 

30-. 
--- , elementary calculation. Dostor, G. 

Arch. Mth. Ps. 56 (1874) 298-. 
--- , theory. Roche, . Gergonne A. 

Mth. 18 (1827-28) 19-. 
-- , hexagonal. Noel, J. N. Quetelet 

Cor. Mth. 5 (1829) 347-. 

, triangular, square and oblong, formula. 
Hubbell, H. Franklin I. J. 34 (1857) 20-. 

Polygons, sums of numbers arranged on. 

Romero, J. N. A. Mth. 1 (1882) 46-. 
Polynomials expressing sums of powers of 

series of natural numbers. Appell, P. N. 

A. Mth. 6 (1887) 312-. 
Powers, formation from arithmetical pro- 

gressions. Wheatstone, (Sir) C. E. S. P. 

7 (1854-55) 145-. 

, ---- . Cantor, M. N. A. Mth. 14 
(1855) 229-. 

Product of first n numbers. Mandart, H. 

Mathesis 19 (1899) 221-. 
--- n quantities expressed in sums of their 

powers. Day, H. G. Mess. Mth. 5 (1871) 

13. 



pansion. Schldfli, L. [1866] Crelle J. 67 
(1867) 179-. 

H.^.a 3 ...*!*. Glaisher, J. W. L. [1877] 
Mess. Mth. 7 (1878) 43-. 

n! expression by an integral function. 
Hadamard, J. Ell. Sc. Mth. 19 (1895) 69-. 

Progression, arithmetical, sum of like powers 
of terms. Ducci, E. G. Mt. 32 (1894) 348-. 

, , -- squares of terms by aid of poly- 
gon. Romero, J. N. A. Mth. 1 (1882) 46-. 

, fractional arithmetical, summation of in- 
tegers. Simerka, V. Casopis 5 (*1876) 39-, 
82- ; Fschr. Mth. (*1876) 86. 

, geometrical, numbers in. Blacklewar, C. 
E. S. P. 3 (1832) 139. 

, , 1, 3, 9, <fec. Unferdinger, F. Grunert 
Arch. 33 (1859) 106-. 



1625 



Progressional series, summation. Benwell, 

J. B. Tilloch Ph. Mg. 58 (1821) 265-. 
Progressions, arithmetical. Elefanti, F. E. 

S. P. 10 (1859-60) 1-. 
, and geometrical. Pedersen, H. A. 

Mth. Ts. 1 (1859) 17-. 
, , when 71 is fractional. Helmes, J. 

Grunert Arch. 35 (1860) 136-. 

by differences. Sardi, C. G. Mt. 11 (1873) 
123-. 

Eational fraction, formula of Laplace's. Jur- 

gemen, C. Crelle J. 11 (1834) 136-. 
Eecurrence, formula. Thomae, J. Crelle J. 

Mth. 110 (1892) 78-. 
Eecurrences, system of combined. Degen, 

C. F. [1819] St. Pet. Ac. Sc. Mm. 9 

(1819-20) 130-. 
Eecurring series. Malfatti, G. F. Verona S. 

It. Mm. 3 (1786) 571-. 
. Svanberg, A. F. Ups. N. Acta S. Sc. 

11 (1839) 1-. 
. Whittcorth, W. A. [1865] Mess. Mth. 

3 (1866) 117-. 
. Ocagne, M. d'. Par. S. Mth. fill. 14 

(1886) 20- ; N. A. Mth. 9 (1890) 93- ; Par. 

EC. Pol. J. 64 (1894) 151-. 
. Netto, E. Mh. Mth. Ps. 6 (1895) 

285-. 

an4 bilinear forms. Study, E. Mh. 
Mth. Ps. 2 (1891) 23-. 

, conditions that scale should be irre- 
ducible. Maillet, E. N. A. Mth. 14 (1895) 
152-, 197-. 

connected with equation 2x 2 = 7/ 2 -l. 
Catalan, E. C. As. Fr. C. E. 12 (1883) 
98-. 

, elementary theory. Ocagne, M. d'. N. 

A. Mth. 3 (1884) 65-. 
and equations. Laisant, C. A. Bll. Sc. 

Mth. As. 5 (1881) 218-. 
, general term, and Euler's expression for 

same. Degen, C. F. [1821] Kiob. Dn. Vd. 

Selsk. Afh. 1 (1824) 135-. 
, geometric representation. Scherk, H. F. 

Brem. Ab. 1 (1868) 225-. 
and indeterminate analysis. Maillet, E. 

As. Fr. C. E. (1895) (Pt. 2) 233-. 
, integration. Longchamps, G. de. As. 

Fr. C. E. (1885) (Pt. 2) 94-. 
leading to continued fractions. Scheib- 

ner, W. Leip. B. 16 (1864) 44-. 
, problem. Degen, C. F. [1819] St Pet. 

Ac. Sc. Mm. (1821-22) 71-. 
, problems. Weiss, A. Crelle J. 38 (1849) 

148-. 
for rational fractional function. Degen, 

C. F. (vi Adds.) Kiob. Ov. (1818-19) 4-. 
, and theorem of Lagrange. Gohierre de 

Longchamps, . As. Fr. C. E. 9 (1880) 

91-. 
, theory, addition. Vesz, J. A. (xn) 

Mag. Tud. Ak. Etk. (Mth.) 3 (1875) (No. 1) 

15pp. 

and theory of numbers. Siebeck, H. 
Crelle J. 33 (1846) 71-. 

, type. Ocagne, M. d'. C. E. 104 (1887) 

419-, 534. 



90 



1625 



Finite Summation. Recurring Series 



1625 



Recurring series, use in analysis of equations. 
Frisiani, P. Mil. Effem. As. (1850) 3-. 

systems, generation by a linear differential 
equation. Pincherle, S. Acta Mth. 16 (1892- 
93) 341-. 

, 1st order and 2nd degree. Pincherle, S. 

Em. B. Ac. Line. Ed. 5 (1889) (Sem. 1) 8-, 

323-. 
Eelation I 3 + 2 3 + ... + n 3 = (1 + 2 + ... + n) 2 . 

Gelin, E. Mathesis 14 (1894) 220-. 
Series with alternate law of recurrence. 

Ocagne, M. d>. Par. S. Mth. Bll. 12 (1884) 

78-. 
, doubly recurring. Betti, E. Tortolini A. 

8 (1857) 48-. 

of Fibonacci, on [u n + l=u n + u n -l]. 
Cesaro, E. G. Teix. J. Sc. 6 (1885) 17-. 

, Fibonacci, peculiarities. Fontes, . As. 

Fr. C. B. (1894) (Pt. 2) 217-. 
, general term found as with recurring series. 

Andre, D. Par. EC. Norm. A. 7 (1878) 

375-. 
, geometrical, fractional number of terms. 

Choquet, C. N. A. Mth. 1 (1842) 74-. 

of quotients, Euclid's summation. Zeuthen, 
H. G. (xn) Ts. Mth. 6 (1876) 168-, 181- ; 
6 (1882) 97- ; 1 (1883) 145-. 

, self-repeating. Warburton, H. Camb. Ph. 

S. T. 9 (1856) (Pt. 4) 471-. 
, whose series of differences are recurring. 

Raabe, J. L. Baumgartner Z. 6 (1829) 

307-. 
, summation. (Dienger, Grunert Arch. 8 

213-214.) Arndt, F. Grunert Arch. 8 (1846) 

383-. 
, of certain. Tait, P. G. Edinb. Mth. 

S. P. 3 (1885) 107-. 
, class. Ocagne, M. d'. C. B. 115 

(1892) 790-, 904. 
, , successive. Dantas Pereira, J. M. 

Lisb. Mm. Ac. So. 2 (1799) 168-. 
Sum of a combinatory series, properties. 

Unferdinger, F. Grunert Arch. 26 (1856) 

227-. 

cubes = a square. Catalan, E. C. [1866] 

. Rm. At. N. Line. 20 (1867) 1-, 77-. 

of secondary numbers, theorem. 
Barbier, E. Bll. Sc. Mth. As. 7 (1883) 42-. 

first n products of p consecutive numbers. 

Laisant, A. N. A. Mth. 6 (1867) 366-. 
products of n quantities taken m together. 

Trowbridge, D. Des Moines Anal. 1 (1874) 

154-. 

r different terms of series. 
Hammond, J. L. Mth. S. P. 7 (1875-76) 
119-. 

reciprocals. Bouvier, L. C. Gergonne 

A. Mth. 15 (1824-25) 39-. 

. Blissard, J. QJ. Mth. 6 (1863) 

242-. 
. Worontzof, M. M. QJ. Mth. 8 

(1867) 185-, 310-. 
of first 1000 integers. Adams, J. C. 

B. A. Bp. (1877) (Sect.) 14-. 
Summation of series, general term of which is 

na n , a being a given number. Bertrand, J. 
N. A. Mth. 8 (1849) 354-. 



Summation of terms of recurring series, forma- 
tion of integers by. Maillet, E. As. Fr. 
C. B. (1896) (Pt. 2) 78-. 

Summations, successive, l m + 2 m + 3 m + . . . x m . 
Lucas, E. [1877] Mess. Mth. 7 (1878) 

Sums of 4 algebraic series. Glaisher, J. W. L. 

[1877] Mess. Mth. 7 (1878) 119-. 
powers of reciprocals of integers. Schlo- 

milch, O. X. Leip. Mth. Ps. B. 29 (1877) 

106-. 

products of an arithmetical progres- 
sion, taken 2, 3, 4 ... together, calculation. 
Lampe, E. Fschr. Mth. (1893-94) 409. 

natural numbers. Mollame, V. 

N. A. Mth. 5 (1886) 364-. 
numbers, theorem. Lerch, . 

G. Teix. J. Sc. 8 (1887) 161-. 

series l n + 2 + . . . x n , l n - 2 n + . . . x n . 
Glaisher, J. W. L. QJ. Mth. 30 (1899) 
166-. 



Special series. 



Collins, E. St Pet. Ac. Sc. Mm. 8 (1817-18) 

242-. 

Schlomilch, O. Grunert Arch. 10 (1847) 342-. 
Thacker, A. Camb. and Dubl. Mth. J. 5 (1850) 

243-. 

Mourgues, , N. A. Mth. 10 (1851) 78-. 
Catalan, E. C. N. A. Mth. 15 (1856) 230-. 
Siacci, F. (vm) A. Mt. 4 (1861) 46-. 
Lucas, E. N. A. Mth. 9 (1870) 49-. 
Amigues, E. N. A. Mth. 10 (1871) 79-. 
Dostor, G. Arch. Mth. Ps. 54 (1872) 70-; 

57 (1875) 222-. 
Lampe, E. [1877] Crelle J. Mth. 84 (1878) 

270-. 

Lucas, E. N. A. Mth. 16 (1877) 18-. 
Pelndr, M. Casopis 6 (*1877) 279-; Fschr. 

Mth. (*1877) HO-. 
Dostor, G. Arch. Mth. Ps. 63 (1879) 435-; 

64 (1879) 310-. 

Marchand, D. N. A. Mth. 20 (1881) 140-. 
Schier, 0. Wien Ak. Sb. 85 (1882) (Ab. 2) 

503-. 
Boije af Gennas, C. 0. Stockh. Ak. Hndl. 

Bh. 10 (1885) No. 4, 6 pp. 
Slavik, J. Casopis 16 (1887) 121- ; Fschr. 

Mth. (1887) 240. 

Locchi, E. Mh. Mth. Ps. 4 (1893) 85-. 
Nielsen, N. N. Ts. Mth. 4 (B) (1893) 1-; 

Fschr. Mth. (1893-94) 410-. 
Barbette, E. Mathesis 14 (1894) 105-. 
Jung, V. Casopis 28 (1899) 124- ; Fschr. Mth. 

(1899) 247. 

Tr 3 . 

r=l 

Genocchi, A. A. Mt. 7 (1865) 151-. 
Cantor, M. Z. Mth. Ps. 11 (1866) 248-; 12 
(1867) 170-. 



91 



1630 Finite Summation 

Unferdinger, F. Arch. Mth. Ps. 48 (1868) 

Amigues, E. N. A. Mth. 10 (1871) 117-. 
Glaisher, J. W. L. Mess. Mth. 4 (1875) 168-. 
Eocquigny, F. [G.] de. Les Mondes 51 (1880) 

153-. 
geometrical summation. Glaisher, J. W. L. 

(vn) [1873] Mess. Mth. 3 (1874) 5. 
problem of Boncompagni, solution. Matthies- 

sen, L. Z. Mth. Ps. 13 (1868) 348-. 



Bretschneider, C. A. Grunert Arch. 1 (1841) 

415-. 

Borchardt, C. W. Berl. Mb. (1857) 301-. 
Brioschi, F. [1857] Tortolini A. 1 (1858) 43-. 
Dostor, G. Arch. Mth. Ps. 64 (1879) 353-. 



Dostor, G. Arch. Mth. Ps. 64 (1879) 356-. 



Puiseux, V. Liouv. J. Mth. 11 (1846)477-. 
Gilbert, P. N. A. Mth. 8 (1869) 434-. 
formulae. Lionnet, E. N. A. Mth. 1 (1842) 

175-. 
. Rispal, A. N. A. Mth. 6 (1847) 273-. 

"2" (a + n - 1) fc-i, "i" [a + n - 1]<* M*-i. 
n _Pepin (lepere). N^A. Mth. 15 (1856) 27-. 
2 (x + ih)n, *~2 (-l) i (* + tft)'. Bjorling, 

JE. G. Stockh!lk. Hndl. 2 (1857-58) 18 pp. 

2 f-j , Jacobian formula involving. Stern, 

M. A. Crelle J. Mth. 84 (1878) 216-. 
r=2+l 

S r 2 or r 3 . Dostor, G. Arch. Mth. Ps. 64 

(1879) 361-. 
F(r). Dostor, G. 
r= 459-, 513-. 
2 (2r 2 ) and 2 (2r- I 2 "*). Glaisher, J. W. L. 

Mess. Mth. 20 (1891) 172-. 
2 (r 2 ). Glaisher, J. W. L. Mess. Mth. 20 

(1891) 120- r 28 (1899) 29-. 



N. A. Mth. 18 (1879) 



1630 Probabilities (including 
combination of observations). 
Theory of errors. 

Accuracy of recollection, measurement. Cat- 
tell, J. McK. Science 2 (1895) 761-. 

Approximate formulae relating to large num- 
bers. La Place, P. S. (Marquis) de. Par. 
Mm. de PI. (1809) 353-, 559-. 



Probabilities 1630 

Approximations, numerical. Guyou, . N. 
A. Mth. 8 (1889) 165-. 

Arithmetical events, study. Cesaro, E. Brux. 
Mm. Cour. 4. 47 (1886) No. 9, 14 pp. 

Association ratios (of phenomena in observa- 
tions). Doolittle, M. H. Smiths. Misc. 
Col. 33 (1888) Art. 4, 83-, 94-. (Wash. Ph. 
S. Bll. 10 (1888).) 

Averages, theory. Local probability. Doo- 
little, M. H. Wash. Ph. S. Bll. 11 (1892) 
596-. 

Bernoulli's inverse theorem. Meyer, A. Brux. 
Ac. Bll. 23 (1856) 148-. 

theorem. Mansion, . Brux. S. Sc. A. 
16 (1892) (Pt. 1) 85-. 

. Goedseels, . Brux. S. Sc. A. 19 

(1895) (Pt. 1) 4-. 
. Mansion, . Brux. S. Sc. A. 22 

(1898) (Pt. 1) 3-. 

. Eayleigh, (Lord). Ph. Mg. 47 (1899) 

. ' Eggenberger, J. Z. Mth. Ps. 45 (1900) 

43-. 
and approximate probability. Nekrasov, 

P. A. [1898] Eec. Mth. (Moscou) 20 (1899) 

485-, 535-; Fschr. Mth. (1899) 214, 215. 
binomial coefficients. Nasimov, P. S. 

Fschr. Mth. (1888) 211. 
, gamma-functions and Laplace's integral. 

Eggenberger, J. Bern. Mt. (1893) 110-, 236. 
, inversion. Monro, C. J. (x) L. Mth. 

S. P. 5 (1873-74) 74-, 145-. 
, . Nekrasov, P. A. Mosc. S. Sc. Bll. 

65 (No. 1) (1890) 45-; Fschr. Mth. (1890) 

235. 
, , simple proof. Gosiewski, W. Krk. 

Ak. (Mt.-Prz.) Ez. 13 (1886) 153- ; Fschr. 

Mth. (1885) 176-. 
, proof by Euler's summational formula. 

Lagrange, C. Brux. Ac. Bll. 31 (1896) 

439-. 
, repeated application. Andrade, J. C. R. 

116 (1893) 1281-, 1482. 
Best reading of an instrument for measuring a 

given quantity. Baum, F. G. Ps. Rv. 8 

(1899) 181-. 

Betting on races. Du Chatenet, M. N. A. 

Mth. 5 (1886) 327-, 380-, 408-. 
Bravais's formulae for regression, etc., with 

skew correlation. Yule, G. U. R. S. P. 60 

(1897) 477-. 
Broken diamond, problem. Cesaro, E. G. 

Mt. 24 (1886) 124-. 
Buffon's problem of the needle. Barbier, E. 

Liouv. J. 5 (1860) 273-. 
. Sylvester, J. J. Acta Mth. 

14 (1890-91) 185-. 
Causation process, results. Paterson, J. Am. 

As. P. (1856) 29-. 
Chance. Whitwarth, W. A. [1871] Mess. Mth. 

1 (1872) 163-. 

and choice, problems supplementary to. 
Whitworth, W. A. Mess. Mth. 4 (1868) 
152-, 193-. 

, continuity. Davis, E. W. [1897] Nebr. 

Un. Stud. 2 (1894-1902) 131-. 
, doctrines. Saint, W. Nicholson J. 21 

(1808) 204-. 



92 



1630 



Probabilities. Theory of Errors 



1630 



Chance, doctrines. Opsimath. [Pseud.] Nichol- 
son J. 21 (1808) 210-. 
, , doubts respecting. Opsimath. [Pseud.] 

(vi Adds.) Nicholson J. 21 (1808) 66-. 
Chances, determination of e x as a limit in 

calculation of. Andrade, . Par. EC. Pol. 

J. 64 (1894) 225-. 
, doctrine. H., B. (vi Adds.) Nicholson 

J. 21 (1808) 121-. 

, , calculation in. Young, Dr T. Nichol- 
son J. 18 (1807) 116-. 
, paradox in. Gallon, F. Nt. 49 (1893-94) 

365-. 
, . Shorter, L. E. Nt. 49 (1893-94) 

413. 
, problem. Day, H. G. QJ. Mth. 9 (1868) 

354-. 
, , experimental solution. Mendenhall, 

T. C. Am. As. P. (1879) 190-. 
, problems. Wilson, J. M. Ph. Mg. 31 

(1866) 170-. 
, theory in Boole's laws of thought. Wilbra- 

ham, H. Ph. Mg. 7 (1854) 465-. 
, , reply to Wilbraham. Boole, G. Ph. 

Mg. 8 (1854) 87-. 
Chessboard, chance of each piece cheeking 

king. Taylor, H. M. Ph. Mg. 1 (1876) 

221-. 
, use for solution of problems in probability. 

Delannoy, H. As. Fr. C. E. (1889) (Pt. 2) 

43-; (1895) (Pt. 2) i 70-. 
Combination of deviations. Ocagne, M. d'. 

N. A. Mth. 14 (1895) 133-. 
measures of one magnitude. Bertrand, J. 

C. E. 106 (1888) 701-. 
observations. Frisiani, P. [1859] Mil. 

I. Lomb. Mm. 11 (1870) 21 pp. 
. Lipschitz, R. C. E. Ill (1890) 

163-. 
. Pizzetti, P. Geneva Un. At. [11] 

(1892) 113-. 
. Levanen, S. Helsingf. Ofv. 37 

(1895) 19-; Fschr. Mth. (1895) 246. 
. Equations, linear, resulting from 

observations of equal weight, solution. San- 

tini, G. [1869] Yen. Mm. I. 14 (1868) 477-. 
, theory. Gauss, C. F. Gott. Cm. 5 

(1819-22) 33-, 63-; 6 (1823-27) 57-; 7 (1828- 

31) 89-. 
, . Donkin, W. F. Ashmol. S. T. 

(1844) 71 pp.; Liouv. J. Mth. 15 (1850) 

297-. 
, . Kleiber, I. A. Kazan S. Nt. 

(Ps.-Mth.) P. 6 (1888) 148- ; Fschr. Mth. 

(1888) 220-. 
, , Gauss's. Nasimov, P. S. Fschr. 

Mth. (1889) 218-. 
_. Kriiger, L. Gott. Nr. (1897) 

146-. 
, , generalised. Newcomb, S. Am. 

J. Mth. 8 (1886) 343-. 
, weights of British noblemen during 

last three generations. Galton, F. Nt. 29 

(1884) 266-. 
Combinations and factorial numbers, theorems. 

Catalan, E. Brux. Ac. Bll. 25 (1893) 238-, 

430-. 



Combining probabilities of same event, possi- 
bility. Terrot, C. H. [1856] Edinb. E. S. 
T. 21 (1857) 369-. 

Comparison of probabilities that are functions 
of one variable. Blaschke, E. Wien Ak. D. 
54 (1888) (Ab. 2) 105-. 

Compensation, arithmetic mean in calculating. 
Dorna, A. Tor. At. Ac. Sc. 4 (1868-69) 757-. 

of errors. Lorenz, L. V. (xn) Ts. Mth. 2 
(1872) 1-, 125-. 

. Zachariae, G. (xn) Ts. Mth. 2 

(1872) 97-, 182-. 
. Bruns, H. Leip. Mth. Ps. Ab. 13 

(1887) 515-. 
, effect of weights. Paucker, M. G. 

von. Mitau Arb. Kurland. Gs. 9 (1851) 183-. 
, Laplace's method. Dienger, J. [1874] 

Wien Ak. D. 34 (1875) (Ab. 2) 21-. 
, a law of duality in. Reina, V. Tor. 

Ac. Sc. At. 29 (1894) 433-. 
proportional errors. Jung, G. Mil. I. 

Lomb. Ed. 13 (1880) 238-. 
Conscription, drawing of lots in, problem 

arising from. Rasch, J. W. N. Arch. Wisk. 

1 (1895) 206- ; Fschr. Mth. (1893-94) 342-. 
Constant aberrations in shooting, precession of 

shot. Cranz, C. D. Nf. Vh. (1897) (Th. 2, 

Halfte 1) 6. 
Continued fractions, application to calculation 

of probabilities. Markov, A. A. Kazan S. 

Ps.-Mth. Bll. 9 (1900) 29-; Fschr. Mth. 

(1899) 215. 

, probability of appearance of given 
number. Wiman, A. Stockh. Ofv. (1900) 
829-. 

, numbers of given magnitude. 

Broden, T. Stockh. Ofv. (1900) 239-. 
Correlated averages. Edgeworth, F. Y. Ph. 

Mg. 34 (1892) 190-. 

, new method of treating. Edgeicorth, 
F. Y. Ph. Mg. 35 (1893) 63-. 

Correlation of averages for four variables, 
example. Bryant, (Mrs) S. Ph. Mg. 36 
(1893) 372-. 

between organs, note on calculation. Edge- 
worth, F. Y. Ph. Mg. 36 (1893) 350-. 

Criterion that given deviations for correlated 

variables may have arisen from random 

sampling. Pearson, K. Ph. Mg. 50 (1900) 

157-. 
Crofton, integral of. Petrini, H. Ts. Mth. 

6 (1889) 39-; Fschr. Mth. (1888) 305-. 
Curve of errors, quadrature. Gram, J. P. 

(xn) Ts. Mth. 1 (1883) 65-; Fschr. Mth. 

(1884) 242. 
Definite integral, evaluation by theory of 

probabilities. Schoute, P. H. As. Fr. C. E. 

(1880) 258-. 
, form for series in theory of probabilities. 

Carpmael, C. [1885] Cn. E. S. P. & T. 3 

(1886) (Sect. 3) 101-. 

integrals and application to probabilities. 
La Place, P. S. (Marquis) de. Par. Mm. de 
l'I. (1810) 279-. 

Determination of ie by needle throwing. 
Levanen, S. Helsingf. Ofv. 34 (1892) 36-; 
Fschr. Mth. (1892) 203. 



93 



1630 



Probabilities. Theory of Errors 



1630 



Determination of some unknowns in geodesy. 
Berardinis, G. de. G. Mt. 25 (1887) 313-. 

unknowns by a large number of approxi- 
mate equations of 1st degree. Cauchy,A. L. 
C. E. 36 (1853) 1114-. 

Development of Lp + (l--.p)] m approximates to 
probability curve as m increases. De Forest, 

E. L. Des Moines Anal. 6 (1879) 65-. 
Digits, relative frequency in natural numbers. 

Newcomb, S. Am. J. Mth. 4 (1881) 39-. 
Distribution of frequency of barometric heights. 

Pearson, K., & Lee, A. [1897] Phil. Trans. 

(A) 190 (1898) 423-. 
points on a line. Bartlett, W. P. G. 

Camb. (M.) Mth. M. 1 (1859) 84-. 
signs of residual errors. Seeliger, H. 

[1879] As. Nr. 96 (1880) 49-. 
Division, eventualities in. Cesaro, E. A. Mt. 

13 (1885) 269-. 

of a straight line, probability problem. 
Berg, F. J. van den. N. Arch. Wisk. 18 
(1891) 42-; Fschr. Mth. (1891) 233-. 

Duration of play. Delannoy, . Par. S. 

Mth. Bll. 16 (1888) 124-. 
, problem. Rouche, E. C. R. 106 

(1888) 47-. 
, . MacMahon (Maj.) P. A. L. 

Mth. S. P. 20 (1889) 195-. 

, , demonstration. Bertrand, . 
C. E. 106 (1888) 49-. 

, some questions of. Rouche, E. 
C. E. 106 (1888) 253-. 

Earthquakes, lunar and solar periodicities. 

Schuster, A. Nt. 56 (1897) 321. v 
Ellipse of error, theory. Czuber, (or Cuber) E. 

[1880] Wien Ak. Sb. 82 (1881) (Ab. 2) 698-. 

or hyperbola, questions of probability. 
Cesaro, E. G. Mt. 22 (1884) 44-. 

Equation, 2nd order, probability that roots are 

real. Bouniakou-sky , V. [1835] St Pet. 

Ac. Sc. Mm. 3 (1838) 341-. 
Equations, 1st order, in number greater than 

number of unknowns; geometrical applica- 
tions. Terquem,0. N. A. Mth. 5 (1846) 551-. 
, normal, solution by indirect elimination. 

Schott, C. A. U. S. Coast Sv. Ep. (1855) 

255-. 
Error function and symmetric functions. 

Thiele, T. N. Kjb. Ov. (1899) 135- ; 

Fschr. Mth. (1899) 216-. 
, law of. Edgeworth, F. Y. Ph. Mg. 16 

(1883) 300-. 

, . Venn, J. Nt. 36 (1887) 411-. 

, . Edgeworth, F. Y. Nt. 36 (1887) 

482-. 
, . Backhouse, T. W. Nt. 36 (1887) 

531. 
, . Schols, C. M. Amst. Ak. Vs. [1] 

(1893) 194- ; Fschr. Ps. (1893) (Ab. 1) 16-. 
, , in case of correlated variations. 

Burbury, S. H. B. A. Ep. (1895) 621-. 
, , compound. Edgeicorth, F. Y. 

Ph. Mg. 41 (1896) 207-. 
, , and correlated averages. Edgeworth, 

F. Y. Ph. Mg. 34 (1892) 429-, 518-. 

, , when differences of observations are 

large. Oudemam, J. A. C. Amst. Ak. Vs. 
[2] (1894) 12-. 



Error, law of, and elimination of chance. 

Edgeworth, F. Y. Ph. Mg. 21 (1886) 308-. 
, , empirical proof. Edgeworth, F. Y. 

Ph. Mg. 24 (1887) 330-. 
, facility of. Watson, H. W. Birm. 

Ph. S. P. 7 (1889-91) 289-. 
, for geometric mean. M'Alister, 

D. B. A. Ep. (1879) 267. 

, of, in sum of n independent 

quantities each accurate to nearest degree. 

Carpmael, C. (xn) [1882] On. E. S. P. & 

T. 1 (1883) (Sect. 3) 9-. 
, frequency. Tait, P. G. [1865] 

Edinb. E. S. T. 24 (1867) 139-. 
, . Galton,F. Ph. Mg. 49 (1875)33-. 

in position of a point in space. De Forest, 

E. L. Conn. Ac. T. 6 (*1882-85) 123-. 
, theory. De Forest, 

E. L. Des Moines Anal. 9 (1882) 33-, 65-. 

target shooting. De Forest, E. L. 
Conn. Ac. T. 7 (1885-88) 1-. 

Errors, accidental, Gauss' law, proof. Gosi- 
ewski, W. Prace Mt.-Fiz. 2 (1890) 223-; 
Fschr. Mth. (1890) 235. 

__ ( _, law. Pellerin, . As. Fr. C. E. 
(1898) (Pt. 2) 156-. 

, , points in theory. Faye, H. C. E. 
106 (1888) 783-. 

, actual and probable, of interpolated values 
derived from tables by means of first differ- 
ences. Woodward, M. S. Des Moines Anal. 
9 (1882) 143-, 169-. 

, determination of modulus. Edgeworth, 

F. Y. Ph. Mg. 21 (1886) 500-. 

in 2 dimensions, law of facility. De Forest, 
E. L. Des Moines Anal. 8 (1881) 3-, 41-, 
73-. 

, distribution of residual, after combination. 

Seeliger, H. Munch. Ak. Sb. 29 (1900) 3-. 
, exercises in calculation. Edgeworth, F. Y. 

Ph. Mg. 36 (1893) 98-. 
, law. Le Maire, A. Brux. S. As. Bll. 

1 (1896) 124-, 207-. 

of observation. Damien, B. C. (xn) Bll. 
Sc. Nord 15 (1883) 121-. 

, extension of law of probability. Adan, 

(Capit.) E. Brux. Ac. Bll. 23 (1867) 148-. 

, formula expressing probability. 
Pizzetti, P. Em. E. Ac. Line. Ed. 5 (1889) 
(Sem. 1) 191 -. 

, formulae for calculation. Maggi, 

G. A. Mil. I. Lomb. Ed. 15 (1882) 351-. 
, law. Kummell, G. H. Des Moines 

Anal. 3 (1876) 133-, 165- ; 6 (1879) 80-. 
, . Bertrand, J. C. E. 106 (1888) 

153-. 
, . Tisserand, E. C. E. 106 (1888) 

231-. 
, . Pizzetti, P. Em. E. Ac. Line. 

Ed. 1 (1892) (Sem. 1) 380-. 
, of facility, and method of least 

squares. Glaisher, J. W. L. As. S. Mm. 

39 (1872) 75-. 
, , proof. Crofton, M. W. [1869] 

Phil. Trans. 160 (1870) 175-. 
, mean error of 2nd order. Paucker, 

M. G. von. Mitau Arb. Kurland. Gs. 8 

(1850) 104-. 



94 



1630 



Probabilities. Theory of Errors 



1630 



Errors of observations, probability of sums of 

powers of, etc. Helmert, F. R. Z. Mth. 

Ps. 21 (1876) 192-. 
, signs of residuals. De Forest, E. L. 

Des Moines Anal. 5 (1878) 65-. 
, , grouping. De Forest, E. L. 

Des Moines Anal. 5 (1878) 1-. 
, theory. De Morgan, A. [1861] 

Camb. Ph. S. T. 10 (1864) 409-. 
, . Lorenzcmi, G. Padova Ac. At. 

e Mm. 5 (1889) 203-. 
, . Czuber, E. Mh. Mth. Ps. 1 

(1890) 457-. 
, . Veltmann, W. As. Nr. 131 

(1893) 1-. 
, , theorems. Winckler, A. Wien 

Sb. 53 (1866) (^6. 2) 6-. 
, physical basis for theory. Burton, C. V. 

L. Ps. S. P. 10 (1890) 276-; Ph. Mg. 28 

(1889) 480-. 

in plane and space. Schols, C. M. [1874- 
86] Amst. Ak. Vh. 15 (1875) 67 pp. ; Delft 
EC. Pol. A. 2 (1886) 123-. 

, demonstration of law. Schols, 

C. M. Delft EC. Pol. A. 3 (1887) 195-. 

, relative and absolute. Gaucherel, E. N. 
A. Mth. 14 (1855) 145 -. 

} _ t theory. Jaufroid, B. N. A. Mth. 15 
(1856) 154-. 

from single causes, composition. Kummell, 
C. H. As. Nr. 103 (1882) 177-. 

, theory. Estienne, . C. K. 130 (1900) 

66-. 
, , application to levelling. Ocagne, M. d'. 

C. E. 120 (1895) 717-. 

, , correction formulae for series of observa- 
tions. De Forest, E. L. Des Moines Anal. 

4 (1877) 79-, 107-. 
, , corrections, repeated, limit. De Forest, 

E. L. Des Moines Anal. 5 (1878) 129-. 
, , , , of terms of series. De Forest, 

E. L. Des Moines Anal. 5 (1878) 65-. 
, , , unsymmetrical, of terms of series, 

and their limits. De Forest, E. L. Des 

Moines Anal. 6 (1879) 140-, 161- ; 7 (1880) 

1-. 
, , criticism of formula of Gauss. Czuber, 

E, Mh. Mth. Ps. 2 (1891) 459-. 
, , elementary. De Forest, E. L. Des 

Moines Anal. 8 (1881) 137-. 
, , foundations. Miiller, F. Mh. Mth. 

Ps. 2 (1891) 61-. 
, , function occurring in. Moser,C. Sch. 

Nf. Gs. Vh. (1898) 45-. 
, , and method of least squares. Goedseels, 

E. [1896] Brux. S. As. Bll. 1 (1896) 253- ; 

2 (1896-97) 6-. 
, , removal of "side coefficients." 

Kummell, . Smiths. Misc. Col. 33 (1888) 

Art. 3, 41. (Wash. Ph. S. Bll. 8 (1885).) 
, , singular law in. Bertrand, J. C. E. 

105 (1887) 779-, 
, , test by target shooting. Kummell, C. 

H. Smiths. Misc. Col. 33 (1888) Art. 1, 

138-. (Wash. Ph. S. Bll. 6 (1884).) 
Evolution, mathematical theory. Pearson, K. 

[1893] Phil. Trans. (A) 185 (1895) 71-. 



Evolution, mathematical theory. (Skew varia- 
tion in homogeneous material.) Pearson, K. 
[1895] Phil. Trans. (A) 186 (1896) 343-. 

, . (Eegression, heredity, and pan- 
mixia.) Pearson, K. [1895] Phil. Trans. 
(A) 187 (1897) 253-. 

, . (Eeproductive selection.) Pearson, 

K. E. S. P. 59 (1896) 301-. 

, . (Telegony in man, etc.) Pearson, 
K. [1896] E. S. P. 60 (1897) 273-. 

, . (Spurious correlation.) Pearson, K. 

E. S. P. 60 (1897) 489-. 

, . ( .) Galton, F. E. S. P. 60 

(1897) 498-. 

, . (Eelative variation and correlation 

in civilised and uncivilised races.) Lee, (Miss) 
A., & Pearson, K. E. S. P. 61 (1897) 343-. 

, . Pearson, K., d- Filon, L. N. G. 

[1897] Phil. Trans. (A) 191 (1898) 229-. 

, . (Speeds of American trotting horses 

as hereditary data.) Galton, F. [1897] 
E. S. P. 62 (1898) 310-. 

, . (Law of ancestral heredity.) 
Pearson, K. E. S. P. 62 (1898) 386-. 

, . (Inheritance of cephalic index.) 
Fawcett, (Miss) C. D., & Pearson, K. 
E. S. P. 62 (1898) 413-. 

, . (Eeconstruction of stature of pre- 
historic races.) Pearson, K. [1898] Phil. 
Trans. (A) 192 (1899) 169-. 

, . (Genetic selection.) Pearson, K. 
[1898] Phil. Trans. (A) 192 (1899) 257-. 

, . (Inheritance of fertility in man.) 

Pearson, K., & Lee, A. [1898] Phil. Trans. 
(A) 192 (1899) 279-. 

, . (Inheritance of fecundity in thorough- 
bred racehorses.) Pearson, K., & Bramley- 
Moore, L. [1898] Phil. Trans. (A) 192 (1899) 
290-. 

, . (Inheritance of characters not 
quantitatively measurable.) Pearson, K., & 
Lee, A. [1899] Phil. Trans. (A) 195(1901)79-. 

, . (Magnitude of certain coefficients 

of correlation.) Pearson, K. [1899] E. S. 
P. 66 (1900) 23-. 

, . (Law of reversion.) Pearson, K. 

E. S. P. 66 (1900) 140-. 

, . (Correlation of characters not 
quantitatively measurable.) Pearson, K. 
[1900] Phil. Trans. (A) 195 (1901) 1-. 

, . ( .) Pearson, K. 

E. S. P. 66 (1900) 241-. 

, . (Fertility and homogamy.) Pearson, 

K. E. S. P. 66 (1900) 316-. 
, . Evolution in man. (Correlation 

of skull.) Lee, A., d- Pearson, K. [1900] 

Phil. Trans. (A) 196 (1901) 225-. 
, . (Homotyposis.) Pearson, K. [1900] 

Phil. Trans. (A) 197 (1901) 285-. 
Factorials, theorems deduced from probabilities. 

Godfray, H. Mathematician 3 (1850) 89-. 
Factors for minimum probable error of a mean. 

Caitchy, A.L. C. E. 37 (1853) 326-. 
Finite expansion, with least error. Buchwaldt, 

F. Ts. Mth. 2 (1884) 33-, 192; Fschr. Mth. 
(1884) 186. 

Forestry problem. Clebsch, R. F. A. Crelle 
J. 67 (1867) 248-. 



95 



1630 



Probabilities. Theory of Errors 



1630 



Frequency curve, asymmetrical. Pearson, K. 
Nt. 48 (1893) 615- ; 49 (1893-94) 6. 

-distributions, tabulation of certain. Shep- 
pard, W. F. Ph. Mg. 50 (1900) 393-. 

, laws of calculus. Cesaro, E. Mil. I. 

Lomb. Bd. 24 (1891) 101-. 
, novel case. Pearson, K. B. S. P. 62 

(1898) 287-. 
Game of cards, application of probabilities. 

Dormoy, E. As. Fr. C. B. (1886) (Pt. 1) 83. 
chance, calculation. Trembley, J. Berl. 

Mm. Ac. (1802) 86-. 
, theory of a. Steen, A. (xn) Ts. 

Mth. 3 (1867) 33-. 
Games of chance. Nieuport, C. F. F. de. 

[1818] Brux. Ac. Sc. Mm. 1 (1820) 89-. 
. Babbage, C. [1820] Edinb. B. S. 

T. 9 (1823) 153-. 
. Grebe, E. W. Grunert Arch. 11 

(1848) 441-. 
. Badoureau, A. Bv. Sc. 1 (1881) 

142-. 
. Baccarat. Badoureau, A. Bv. Sc. 

1 (1881) 239-. 
. , theory. Bertezene, A. Bv. Sc. 

7 (1897) 780-. 

. "Bell" and "hammer" game, 
theory. Ekama, H. N. Arch. Wisk. 19 
(1892) 107- ; Fschr. Mth. (1892) 200-. 

. , . Mounier, G. J. D. 

N. Arch. Wisk. 19 (1892) 188- ; Fschr. Mth. 

(1892) 201. 
. Billiards, probabilities at 3-ball 

game. Peirce, B. [1877] Am. Ac. P. 13 

(1878) 141-. 

. "Bouillotte." Dormoy, E. Bv. 

Sc. 40 (1887) 91-. 
. , chances of the "pair royal." 

Lame, G. C. B. 28 (1849) 705-. 
. Dice. Bierem de Haan, D. Amst. 

Ak. Vs. M. 12 (1878) 371- ; Arch. Neerl. 14 

(1879) 370- ; N. Arch. Wisk. 6 (*1880) 49-, 
113-. 

. . Gomoll, J. Arch. Mth. Ps. 

17 (1900) 363-. 

. , calculation of probability. 
Schweigger, F. Z. Nw. 2 (1877) 114-. 

. , odds of throwing specified 
number. Scott, G. Assur. Mg. 4 (*1854) 
247-. 

. , throw with 6. Baur, C. W. 

Z. Mth. Ps. 12 (1867) 355-. 
. Dice-throwing experiments, new set. 

Wolf, R. Ziir. Vjschr. 38 (1893) 10-. 
. Faro, chances for bank. Greisinger, 

G.A. Baumgartner Z. 4 (1828) 210-. 

. Piquet, theory. Badoureau, . 
Bv. Sc. 37 (1886) 299-. 

. Pitch and toss, two ways of finding 

TT. Barbier, E. C. B. 94 (1882) 1461-. 

, risk. Hausdorff, F. Leip. Mth. 

Ps. B. 49 (1897) 497-. 

. Bouge et noir, advantage of bank. 

Oettinger, L. Crelle J. 47 (1867) 327-. 

. Trente-et-quarante, advantage of 
bank. Poisson, S. D. Gergonne A. Mth. 
16 (1825-26) 173-. 



Games of chance. Whist, theory. Badoureau, 

. Bv. Sc. 36 (1885) 587-. 
, probabilities in connection with. Delannoy, 

H. As. Fr. C. B. (1890) (Pt. 2) 29-. 
Gauss's proposition, proof. Rusjan, C. Prace 

Mt.-Fiz. 3 (1892) 49-; Fschr. Mth. (1892) 

205-. 
Geometrical probabilities, theory. Czuber, E. 

Wien Ak. Sb. 90 (1885) (Ab. 2) 719-. 

probability, problem. Pdnek, A. Casopis 
11 (*1882) 121- ; Fschr. Mth. (1882) 179. 

Geometrography applied to different solutions 
of a problem. Lemoine, E. Par. S. Mth. 
Bll. 20 (1892) 132-. 

Geometry, application to problems in pro- 
bability. Simmons, (Rev.) T. C. As. Fr. 
C. B. (1894) (Pt. 2) 266-. 

, . Lemoine, E. As. Fr. C. 

B. (1896) (Pt. 1) 135-. 

, questions of means and probabilities. 

Lalanne, L. L. Chretien-. C. B. 87 (1878) 
355-; Liouv. J. Mth. 5 (1879) 107-, 123-. 

Gravity determination by pendulum, treatment 
of equations. Venturi, A. N. Cim. 11 
(1900) 33-. 

H-curve, so-called. Boltzmann, L. Mth. A. 
50 (1898) 325-. 

Hypergeometric series in connexion with ob- 
servation polygons. Pearson, K. Ph. Mg. 
47 (1899) 236-. 

Impartiality, postulate of, in theory of errors. 
Crotti, F. Mil. I. Lomb. Bd. 28 (1895) 271-. 

Index numbers, accuracy of proposed calcula- 
tion. Edgeworth, F. Y. B. A. Bp. (1888) 188-. 

Inverse probabilities. MakeJuim, W. M. I. 
Act. J. 29 (1892) 242-, 444-. 

, Makeham's theory. Stabler, E. L. 
I. Act. J. 30 (1893) 239-, 580. 

probability. Markow, A. A. Fschr. Mth. 
(1900) 228. 

. Wilson, J.C. [1900] Nt. 63 (1900-01) 

154-, 188. 

, discussion of Laplace's problem. 
Catalan, E. C. Liege S. Sc. Mm. 15 (1888) 
No. 1, 255-. 

Large numbers, approximate calculation of 
functions of. Nekrasov, P. A. [1898-99] 
Bee. Mth. (Moscou) 20 (1899) 431- ; 21 (1901) 
379-; Fschr. Mth. (1898) 187-. 

, law, in theory of probabilities. 
Imseneckij, V. G. Kharkov Mth. S. Com. 
1 (1889) 1-; Fschr. Mth. (1888) 211. 

, and least squares method. Markov, 
A. A. Kazan S. Ps.-Mth. Bll. 8 (1899) 
110- ; 9 (1900) 41-; Fschr. Mth. (1898) 188. 

, , Markov's law. Nekrasov, 

P. A. Kazan S. Ps.-Mth. Bll. 9 (1900) 18-; 
Fschr. Mth. (1899) 215. 

, Poisson's law. Mansion, P. Brux. Ac. 

Bll. 25 (1893) 11-. 

, probabilities depending on, formulae. 
Poisson, S. D. C. B. 2 (1836) 603-. 

Law of the long run. Mendenliatt, T. C. 
Science 2 (1895) 825-. 

Laws of error for situation of points, composi- 
tion of. Ocagne, M. d\ C. B. 118 (1894) 
517-. 



9G 



1630 Probabilities, etc. 

Least-square computation, form of. Farquhar, 
H. Smiths. Misc. Col. 33 (1888) Art. 1, 
150-. (Wash. Ph. S. fill. 6 (1884).) 

fallacies. Safford, T. H. Am. As. P. 

(1892) 57-. 

Least Squares Method. 

Legendre, A. M. Par. Mm. de PI. (1810) 

(pte. 2) 149-. 
Ivory, J. Tilloch Ph. Mg. 65 (1825) 3-, 81-, 

161- ; 68 (1826) 161-. 
Niirnberger, . Gorl. Ab. 1 (1827) 22-. 
Bitnicz, L. Evk. 3 (1838) 42-. 
Bessel, F. W. As. Nr. 17 (1840) 225-, 305-. 
Ellis, R. L. [1844] Camb. Ph. S. T. 8 (1849) 

204-. 

Wolf, R. Bern Mt. (1849) 140-. 
Paucker, M. G. von. [1850] St Pet. Ac. Sc. 

Bll. 9 (1851) 113- ; 10 (1852) 33-, 233-, 

234-. 

Hossard, P. N. A. Mth. 10 (1851) 456-. 
Arrest, H. d\ Leip. B. (1854) 133-. 
Bertrand, J. C. B. 40 (1855) 1190-. 
Wrede, F. J. Stockh. Ofv. 14 (1857) 73-. 
Kurz, A. Ziir. Vjschr. 8 (1863) 225-. 
Todhunter, I. [1865] Camb. Ph. S. T. 11 (1871) 

219-. 
Miller (Miller-Hauenfels), Alb. von. Oestr. Z. 

Brgw. 15 (1867) 181, 194. 
Minding, E. F. A. St Pet. Ac. Sc. Bll. 16 

(1871) 305-. 

Glaisher, J. W. L. Nt. 6 (1872) 140-. 
Jouffret, E. P. Ev. Mar. et Col. 38 (1873) 5-, 

523-, 957; 42 (1874) 665-, 986-; 43 (1874 

131-. 
Wrede, F. J. Stockh. Ofv. 30 (1873) (No. 8) 

3-; (No. 10) 21-. 

Faye,H.A.E. C. E. 80 (1875) 352-. 
Laurent, H. Liouv. J. Mth. 1 (1875) 75-. 
Safford, T. H. Am. Ac. P. 11 (1876) 193-. 
Lorenz, L. V. (xn) Ts. Mth. 6 (1876) 33-. 
Adcock, R. J. Des Moines Anal. 4 (1877) 183- ; 

5 (1878) 21-. 

Glaisher, J. W. L. Mess. Mth. 9 (1880) 132. 
Edgeworth, F. Y. Ph. Mg. 16 (1883) 360-. 
Mansion, P. Brux. Ac. Bll. 9 (1885) 9-. 
Bertrand, J. C. E. 106 (1888) 1115-. 
Yarochenko, S. Bll. Sc. Mth. 17 (1893) 113-. 
Gosieioski, W. Prace Mt.-Fiz. 4 (1894) 103- ; 

Fschr. Mth. (1893-94) 348-. . 
Andrade, J. C. E. 122 (1896) 1400-. 
Goedseels, . Brux. S. Sc. A. 21 (1897) (Ft. 1) 

13-. 
alleged proof. Ellis, R. L. Ph. Mg. 37 (1850) 

321-, 462. 
application. Gauss, C. F. As. Nr. 5 (1827) 

230. 

. Hansen, P. A. As. Nr. 8 (1831) 463-. 
. Argelander, F. W. A. As. Nr. 21 (1844) 

163-. 

. Freuchen, P. Mth. Ts. 3 (1861) 81-. 
. Carvallo, E. C. E. 106 (1888) 924-. 
to the case where the unknown quantity 

satisfies certain exact conditions. Nasimoff, 

P. S. Fschr. Mth. (1889) 219. 
cases of systematic error. Thiele, T. N. 

Kjob. Dn. Yd. Selsk. Skr. 12 (1880) 381-. 



Least Squares Method 1630 

application to conditioned observations. Stein- 
tluil, A. E. Mess. Mth. 10 (1881) 185-. 

of determinants. Geer, P. van. N. Arch. 
Wisk. 1 (*1875) 179-; 9 *1882) 180- ; Arch. 
Neerl. 12 (1877) 229-; 18 (1883) 127-. 

. Gravelaar, N. L. W. A. N. Arch. 

Wisk. 10 (1884) 107-. 
. Zbrozek, D. Krk. Ak. (Mt.-Prz.) 

Pam. 9 (1884) 199-. 

to geodesy. Bache, A. D. Am. As. P. 
(1849) 102-. 

. Hansen, P. A. Leip. Ab. Mth. Ps. 

8 (1868) 571- ; 9 (1871) 1-. 
. Nagel, A. Giving. 42 (1896) 703-. 

to hydraulic problem. Merriman, M. Frank- 
lin I. J. 74 (1877) 233-. 

approximation. Colding, L. A. Kjob. Ov. 

(1857) 52-. 
bibliography and notes. Merriman, M. [1877] 

Conn. Ac. T. 4 (1877-82) 151-. 
Bouniakowsky. Erman,A. Erman Arch. Es. 

19 (1860) 1-. 
case where number of unknowns is large. Nek- 

rasov, P. A. Eec. Mth. (Moscou) 12 (1885) 

189. 
compensation of errors. Pizzetti, P. Em. E. 

Ac. Line. Ed. 3 (1887) (Sem. 2) 230-, 

288-. 
correction of observations. Whitaker, H. Sid. 

Mess. 9 (1890) 458-. 
deduction from calculus of probabilities. 

Reuschle, [C. G.] Crelle J. 26 (1843) 333-; 

27 (1844) 182-. 
(Eeuschle). Encke,J.F. Crelle 

J. 28 (1844) 213-. 
determination of point by system of planes. 

Jung, G. Mil. I. Lomb. Ed. 30 (1897) 

1014-. 
elementary proof. Gosiewski, W. Kosmos 

(Lw.) 20 (1895) 366-; Fschr. Mth. (1895) 

245. 

theory. Tsinguer, . Mosc. Bll. S. Nt. 35 
(1862) (pte. 2) 446-. 

equivalent factors. Bond, G. P. [1856] Am. 

Ac. Mm. 6 (1857) 179-. 

failure, application of method of limiting co- 
efficients. Cauchy, A. L. C. E. 37 (1853) 

150-. 
function <. Landre, C. L. N. Arch. Wisk. 

7 (*1881) 21 1-. 
fundamental theorem. Denzler, W. Ziir. Mt. 

2 (1850-52) 110-. 
Hagen's proof. Merriman, M. Franklin I. J. 

74 (1877) 330- . 
Laplace's discovery. Bienayme, J. C. E. 37 

(1853) 309- . 

proof. Glaisher, J. W. L. Ph. Mg. 43 
(1872) 194-. 

principle, demonstration. Le Grand Roy, E. 
Neuch. S. Sc. Bll. 27 (1899) 23-. 

, elementary discussion. Merriman, M. 
Franklin I. J. 74 (1877) 173-. 

, (Merriman). Kummell, C. H. Frank- 
lin I. J. 74 (1877) 270-. 

of the mean. Lagrange, C. Brux. Ac. Bll. 
32 (1896) 60-. 

principles. Giletta, L. [1879] G. Mt. 18 (1880) 
159-. 



97 



1630 Least Squares Method 

probable error. Liouville, J. Liouv. J. Mth. 

17 (1852) 31-. 
. Bienaymf, J. Liouv. J. Mth. 17 (1852) 

33-; C. B. 37 (1853) 5-; Par. Mm. Sav. Etr. 

15 (1858) 615-. 
problem. Merriman, M. [1891] N. Y. Mth. S. 

Bll. 1 (1892) 39-. 
proof. Matzka, W. Grunert Arch. 11 (1848) 

369-. 

of some relations. Kummell, C. H. Des 
Moines Anal. 7 (1880) 84-. 

reduction of experiments. Harvey, G. Edinb. 

Ph. J. 7 (1822) 292-. 
resolution of system of linear equations with 

three unknowns. Kononowitsch,A.K. Fschr. 

Mth. (1896) 184. 

simplification, in calculation of empiric con- 
stants. Bellati, M. Yen. I. At. 1 (1875) 

849-. 
solution of equations. Gldisher, J. W. L. 

[1874-80] As. S. M. Not. 34 (1874) 311- ; 

40 (1880) 600- ; 41 (1881) 18-. 
by successive approximations. Seidel, 

P. L. von. [1873] Munch. Ak. Ab. 11 (1874) 

(B te Ab.) 81-. 
linear equations. Jacobi, C. G. J. As. 

Nr. 22 (1845) 297-. 
supplement. Wittstein, T. As. Nr. 102 (1882) 

339-. 
theorem, generalisation. Jordan, C. [1872] 

Z. Mth. Ps. 18 (1873) 116-. 
theory. Encke, J. F. Berl. As. Jb. (1834) 

249-; (1835) 253-; (1836) 253-; Berl. B. 

(1850) 211-. 

. Biver,P.E. Liouv. J. Mth. 18 (1853) 169-. 
. Casorati, F. Tortolini A. 1 (1858) 329-. 
. Catalan, E. C. [1878] Brux. Ac. Sc. Mm. 

43 (1882) (No. 3) 42 pp. 
. Lerch, M. Prag Cesk6 Ak. Fr. Jos. Ez. 

(Tfida 2) 1 (1892) Art. 27, 70 pp.; Fschr. 

Mth. (1892) 446-. 
. SleSinskij, I. V. N. Ks. S. Nt. Mm. (Mth.) 

14 (1892) 201- ; Fschr. Mth. (1892) 205. 
, formula in. London, W. J. Nt. 41 (1890) 

394. 
values of constants in equation from the n + 1 

values of y x when x = 0, 1, 2 . . . n. Carpmael, 

C. As. S. M. Not. 39 (1879) 489-. 
weights. Dienger, J. Grunert Arch. 19 (1852) 

197-. 
. Jordan, W. Z. Mth. Ps. 17 (1872) 

350-. 

of 6 elements, general formulae. Fiona, G. 
Lindenau Z. 6 (1818) 249-. 



Linguistic resemblances, accidental, probability. 

Chase, P. E. [1863] Am. Ph. S. T. 13 

(1869) 25-. 
, note. Oliver, J. E. [1864] Am. Ph. S. 

T. 13 (1869) 69-. 
Longitude calculations, determination of mean 

error from differences of double measures. 

Helmert, F. E. As. Nr. 81 (1873) 49-. 
measures, probable error. Dienger, J. 

Grunert Arch. 31 (1858) 225-. 



Probabilities, etc. 1630 

Lottery, state, calculations. Bonicelli, P. (vt 
Adds.) Majocchi A. Fis. C. 20 (1845) 97-. 

Marriage, probable duration. Drobisch, M. W. 
Leip. Mth. Ps. B. 32 (1880) 1-. 

Mathematical expressions of mean temperature 
and mean magnetic intensity. Brewster, 
Sir D. Pogg. A. 21 (1831) 323-. 

and moral expectation. Pdnek, A. Casopis 
6 (*1877) 69-, 122-, 218- ; 7 (1878) 78-; 
Fschr. Mth. (1877) 150. 

Mayer, Tobias, method. Goedseels, P. J. E. 

Brux. S. Sc. A. 24 (1900) (Pt. 2) 37-. 
Mean, arithmetic, errors likely in finding. 

Toschi, A. Palomba Kac. 3 (1847) 312-. 
, principle. Schiaparelli, G. V. As. Nr. 

87 (1876) 55-; 88 (1876) 141-. 
, , . Stone, E. J. As. Nr. 88 (1876) 

61-. 
, , , generalisation. Pizzetti, P. Em. 

E. Ac. Line. Ed. 5 (1889) (Sem. 1) 186-. 
, , in observation results. Schiaparelli, 

G. V. Mil. I. Lomb. Ed. 1 (1868) 771-. 

error. Helmert, F. E. As. Nr. 85 (1875) 
353-. 

of an angle in method of binary combina- 
tions. Jadanza, N. Tor. Ac. Sc. At. 33 
(1897) 643- or 883-; 34 (1898) 698- or 966-. 

. Pizzetti, P. 

Tor. Ac. Sc. At. 34 (1898) 745- or 1013-. 

chain measures. Winckler, A. Schlo- 

milch Z. 6 (1861) 109-. 

, determination. Zachariae, G. As. Nr. 

80 (1873) 67-. 

of a function of observed quantities, 
theorem. Pizzetti, P. Em. E. Ac. Line. 
Ed. 2 (1886) (Sem. 1) 597-. 

observations. Gerling, C. L. Grunert 

Arch. 25 (1855) 219-. 
, theory. Landre, C. L. N. Arch. 

Wisk. 10 (1884) 1-. 
, . Kooten, F. H. van. N. Arch. 

Wisk. 12 (1886) 94-; Fschr. Mth. (1885) 

184. 
for system of observations. Pizzetti, P. 

Em. E. Ac. Line. Ed. 5 (1889) (Sem. 1) 

740-. 
, geometric, law. M'Alister, D. QJ. Mth. 

17 (1881) 175-. 

probabilities applied to statistics. Bertrand, 
J. C. E. 106 (1888) 1311-. 

of successive, observations, calculation. Euf- 
Jini, F. P. (xi) Mod. Ac. Sc. Mm. 8 (1867) 
65-. 

, theorem of the ; the converse of Bernoulli's 
theorem. Lagrange, C. Brux. Ac. Bll. 
(1899) 428-. 

, theory of errors founded on theorem of. 
Lagrange, C. Brux. Ac. Bll. 35 (1898) 795-. 

and true value of polynomial, consequences 
of accepted equality. Bertrand, J. C. E. 
106 (1888) 1259-. 

values. Tchebicheff, P. de. Liouv. J. Mth. 
12 (1867) 177-. 

. Scheibner, W. Leip. B. 25 (1873) 562-. 

. Hayes, E. Science 21 (1893) 333. 

with reference to plane curves and curved 

surfaces. Czuber, E. Arch. Mth. Ps. 6 

(1888) 294-. 



1630 



Probabilities. Theory of Errors 



Mean values, theory. Beeck-Calkoen, J. F. van. 

Amst. Vh. 2 (1816) 1-. 
Means, calculation and scientific applications. 

Segnitz, E. Schlomilch Z. 7 (1862) 65-. 
, choice of. Edgeworth, F. Y. Ph. Mg. 24 

(1887) 268-. 
, method of, applied to transformation, to 

calculation, and to limits of remainders in 

series. Poncelet, J. V. [1833] Crelle J. 13 

(1835) 1-. 

of observations. Trembley, J. Berl. Mm. 
Ac. (1801) 29-. 

. Lloyd, H. [1848] Ir. Ac. T. 22 

(1855) 61-. 
. Cauchy, A. L. C. B. 37 (1853) 

198-, 381-. 

. Brassinne, E. Toul. Mm. Ac. 6 
(1862) 421-. 

Measures, fallible, of variable quantities, and 

meteorological observations. Darwin, G. H. 

Ph. Mg. 4 (1877) 1-. 
Mechanical rectification of an arc of a curve. 

Wiener, C. Z. Mth. Ps. 16 (1871) 112-. 
Michell's problem (distribution of stars). Lup- 

ton, S. Nt. 38 (1888) 272-, 414. 
Moral expectation, maxima and minima. Bunia- 

kovskij, V. Ja. [1879] St Pet. Ac. Sc. Mm. 

(Es.) 36 (*1880) (Suppl.) No. 1, 22 pp. 
Most probable existence, principle. Gosiewski, 

W. Prace Mt.-Fiz. 3 (1892) 55-; Fschr. 

Mth. (1892) 73-. 

mechanical system of the universe. 
Gosiewski, W. Crc. Ac. Sc. Bll. (1889) No. 
5, xli-. 

result of number of observations. Wilson, 

J. M. [1877] As. S. M. Not. 38 (1878) 
81-. 

from observations with assigned 
weights. Stone, E. J. As. S. M. Not. 36 
(1876) 290-. 

-of equal value. Stone, E. J. 

As. S. M. Not. 33 (1873) 570-. 
value of latitude. Flint, A. S. Smiths. 

Misc. Col. 33 (1888) Art. 4, 91-. (Wash. Ph. 

S. Bll. 10 (1888).) 

quantity from n observations with- 
out use of Gauss's postulate. Bervi, N. V. 

Mosc. S. Sc. Bll. 96 (No. 1) (1899) 41-; 

Fschr. Ps. (1900) (Ab. 1) 24. 
unknowns connected by equations 

of condition, calculation. Seidel, P. L. von. 

As. Nr. 84 (1874) 193-. 

values of frequency-constants, calcula- 
tion. Sheppard, W. F. L. Mth. S. P. 29 

(1898) 353-. 
Mountain ranges, application of calculus of 

probabilities. Spottiswoode, W. [1860] Gg. 

S. J. 31 (1861) 149-. 

Nearness of approximation in theory of observa- 
tions. Kooten, F. H. van. Batav. Ntk. Ts. 

49 (1890) 160-. 
Normal distribution and normal correlation. 

Sheppard, W. F. [1897] Phil. Trans. (A) 

192 (1899) 101- . 
Observation-equations, special treatment of 

certain. Woodward, R. S. Smiths. Misc. 

Col. 33 (1888) Art. 1, 156-. (Wash. Ph. S. 

Bll. 6 (1884).) 



1630 

Observation results, numerical, adjustment. 

Sprague, T. B. B. A. Bp. (1883) 446-. 
Observations, a posteriori evaluation of trust- 
worthy character of a series of. Bertrand, J. 

C. B. 106 (1888) 887-. 
, combination of results. Powalky, C. JR. 

As. S. M. Not. 34 (1874) 476-. 
, compensation and mean error. Paucker, 

M. G. von. Mitau Arb. Kurland. Gs. 6 

(1849) 41-; 9 (1851) 183-. 
, corrections of personal error. Fechner, 

G. T. Leip. B. 13 (1861) 57-. 
, determination of accuracy. Gauss, C. F. 

Lindenau Z. 1 (1816) 185-. 
, . Hauber, G. F. Baumgartner Z. 

7 (1830) 286-. 
, direct, calculation of result of system of. 

Pizzetti, P. Liege S. Sc. Mm. 15 (1888) 

No. 3, 32 pp. 
, doubtful. Edgeworth, F. Y. Ph. Mg. 23 

(1887) 364-. 

, , criterion for rejection. Peirce, B. Gould 

As. J. 2 (1852) 161-. 
, , Peirce 's criterion. Gould, B. A. Gould 

As. J. 4 (1856) 81-. 
, , . Airy, G. B. Gould As. J. 4 

(1856) 137-. 
, , (Airy's criticism). Winlock, J. 

Gould As. J. 4 (1856) 145-. 
, , . Peirce, B. Am. Ac. P. 13 

(1878) 348-. 
, , rejection. Stone, E. J. As. S. M. Not. 

28 (1868) 165-. 
, , . Glaisher, J. W. L. As. S. M. 

Not. 33 (1873) 391-. 
, , . Stone, E. J. [1873] As. S. M. 

Not. 34 (1874) 9-. 
, , . Doolittle, . Smiths. Misc. Col. 

33 (1888) Art. 1, 152-. (Wash. Ph. S. Bll. 

6 (1884).) 
, equations of condition. Grunert, J. A. 

Grunert Arch. 21 (1853) 453-. 
, functions of, accuracy. Gerling, C. L. 

Grunert Arch. 38 (1862) 379-. 
, incomplete, introduction into probability- 
calculations. Kiittner, W. Z. Mth. Ps. 29 

(1884) 193-. 
, limits of accuracy. Paucker, M. G. von. 

Mitau Send. Kurland. Gs. 1 (1840) 73-. 
, to measure of precision. Adan, (Capi- 

taine) E. Brux. Ac. Bll. 22 (1866) 480-. 
, methods of detecting unknown inequalities 

in. Stokes, G. G. B. S. P. 29 (1879) 

122-. 
, probable existence of a cause of error in a 

series. Liagre, J. Brux. Ac. Bll. 22 (1855) 

(pte. 2) 15-. 
, mean. Svanberg,J. Stockh. Ak. Hndl. 

(1821) 388-. 
, reduction. Edgeworth, F. Y. Ph. Mg. 17 

(1884) 135-. 

relating to several quantities, new method 
of reducing. Edgeworth, F. Y. Ph. Mg. 25 

(1888) 184-. 

, (Edgeworth's). 

Turner, H. H. Ph. Mg. 24 (1887) 466-. 

represented by diagrams. Earnshaw, S. Ph. 
Mg. 27 (1845) 127-. 

I G2 



1630 Probabilities, etc. 

Observations, results, probable mean. Anon. 
(vi 542) Gergonne A. Mth. 12 (1821-22) 
181. 

, , properties. Quetelet, L. A. J. Brux. 
Ac. Bll. 19 (1852) (pte. 2) 303-. 

, series of, translation into continuous for- 
mulae. Merrifield, C. W. [1880] L. Mth. S. 
P. 12 (1880-81) 4-. 

and statistics. Edgeworth, F. Y. [1885] 
Camb. Ph. S. T. 14 (1889) 138- ; Camb. Ph. 
S. P. 6 (1889) 101-. 

, theory, and method of least squares. 

Thiele, T. N. Bll. Sc. Mth. 14 (1890) 73-. 
, true average. Smith, E. H. Nt. 37 (1888) 

464. 
, values making greatest error a minimum. 

Cauchy, A. L. [1814] Par. EC. Pol. J. 13 

(1831) (20 e cah.) 175-. 
Observed points, new method of representing, 

suitable for explorers. Ldska, V. Prag Sb. 

(1895) (Mth.-Nt.) No. 41, 6 pp.; Fschr. Mth. 

(1895) 248. 
Personal equation. Gonnessiat, F. Lyon Un. 

A. 3 (Fasc. 2) (1892) 167 pp. 
Petersburg problem. Orchard, W. Assur. Mg. 

2 (*1852) 185. 
. Czuber, (or Cuber) E. Arch. Mth. Ps. 

67 (1882) 1-. 
. Catalan, E. C. Lie~ge S. Sc. Mm. 15 

(1888) No. 1, 248-. 

. Wolf, E. Zur. Vjschr. 34 (1889) 264-. 

. Lupton, S. Nt. 41 (1890) 165-. 

. Seydler, . C. E. 110 (1890) 326-. 

, paradox analogous to. Bertrand, J. 
C. E. 105 (1887) 831-. 

Physical laws deduced from empirical curves. 

Pucci, E. N. Cim. 27 (1890) 220- ; 28 

(1890) 111-. 
Plane, calculation of mean situation from more 

than three points. Weisbach, J. Civing. 16 

(1870) 397-. 
Plausible value of a variable magnitude. Es- 

tienne, . C. E. 130 (1900) 393-. 
Points problem. Mansion, P. Brux. Mm. 

Cour. 8. 21 (1870) (No. 1) 13 pp. 
. Badoureau, A. Par. EC. Pol. J. 27 

( = cah. 44) (1874) 123-. 
. Catalan, E. C. Liege S. Sc. Mm. 12 

(1885) No. 2, 65-. 
Position of a point determined by many 

measurements. Hammer, E. Z. Mth. Ps. 

43 (1898) 105-. 
, errors. Dahlander, G. B. Stockh. 

Ofv. 14 (1857) 405- ; 15(1858)49-; 18(1861) 

63-. 
in a plane, composition of law 

of errors for. Ocagne, d'. Par. S. Mth. 

Bll. 23 (1895) 65-. 
, probability of error in. Br avals, A . 

Par. Mm. Sav. Etr. 9 (1846) 255-. 
Pothenot's problem, theory of errors in. 

Andrce, . As. Nr. 47 (1358) 193-. 
Precision of a system of measurements. 

Bertrand, J. L. F. C. E. 106 (1888) 

, determination. Bertrand, 

J. C. E. 106 (1888) 440-. 



Probabilities 1630 

Presumable error in evaluation of the angles 
of a triangle. Bertrand, J. C. E. 106 
(1888) 967-. 

Principle of least action and probability theory, 
connexion between. Gosiewski, W. Prace 
Mt.-Fiz. 1 (1888) 97-; Fschr. Ps. 
(Ab. 1) 253-. 



PROBABILITIES. 

Breevilt, C. [1788] Mengelwerk Wisk. Vh. 1 

(1796) 81-. 
Oettinger, L. Munch. Ab. 2 (1831-36) 199-, 

243-. 

Poisson, S. D. C. E. 2 (1836) 395-. 
Mondesir, E. Liouv. J. Mth. 2 (1837) 3-. 
Bienayme, J. Par. S. Phlm. PV. (1840) 23-. 
Oettinger, L. Grunert Arch. 1 (1841) 113-. 
Hamilton, (Sir) W. B. B. A. Ep. (1843) 

(pt. 2) 3-. 
Oettinger, L. Crelle J. 26 (1843) 217-, 311- ; 

30 (1846) 232-, 296-; 34 (1847) 153- ; 36 

(1848) 221-, 296-; 42 (1852) 213-. 
Bordoni, A. Mil. G. I. Lomb. 4 (1852) 31-. 
Wolf, E. Bern Mt. (1852) 133-. 
Cayley, A. Ph. Mg. 6 (1853) 259. 
Dedekind,R. Ziir. Vjschr. 4 (1859) 346-; 5 

(1860) 66-. 

Cayley, A. Ph. Mg. 23 (1862) 352-, 470-. 
Matthiessen, L. Arch. Mth. Ps. 47 (1867) 

457-. 
Meyer, A. Liege S. Sc. Mm. 4 (1874) (No. 2) 

446 pp. 
Eocquigny, F. [G.] de. Les Mondes 51 (1880) 

652-. 
a priori. Edgeworth, F. Y. Ph. Mg. 18 

(1884) 204-. 

, of errors of observation. Pizzetti, P. 
G. Mt. 27 (1889) 77-. 

accidental errors. Seeliger, H. As. Nr. 97 

(1880) 289-. 
. Gosiewski, W. Prace Mt.-Fiz. 1 (1888) 

1-; Fschr. Mth. (1888)227. 

, (Gosiewski). Baraniecki, M. A. Prace 
Mt.-Fiz. 2 (1890) 220- ; Fschr. Mth. (1890) 
235-. 

. Eussjan, C. N. Es. S. Nt. Mm. 
(Mth.) 9 (1889) 134- ; Fschr. Mth. (1889) 
219-. 

(Eussjan). Sonin, N. J. [1889] Vars. 

S. Nt. Tr. (1889-90) (C. E., Ps. C.) No. 4, 2-. 

, application to educational statistics. 
Maximowitsch, W. P. Fschr. Mth. (1888) 
229. 

adjustment and computation. Lazarus, W. 

I. Act. J. 20 (*1378) 410-. 
analogy, and least squares. Donkin, W. F. 

QJ. Mth. 1 (1857) 152-. 
analysis. Binet, J. P. M. C. E. 19 (1844) 

373-. 
application. Brian, L. Abv. Mm. S. Em. 

(1838-40) 251-. 
. Ghibaldan, I. Bucarest S. Sc. Bll. 

6 (1897) 479- ; 7 (1898) 225- ; 8 (1899) 18-. 

to comparison of causes favouring a re- 
curring phenomenon. Steen, A. Kjob. Ov. 
(1866) 8-. 



100 



1630 Probabilities 

application to dynamical systems. Zermelo, E. 

Ps. Z. 1 (1900) 317-. 
geodesy. La Place, P. S. (Marquis) 

de. Con. des Temps (1820) 422-. 
, levelling operations, &c. La Place, 

P. S. (Marquis) de. A. C. 12 (1819) 337-. 

geodetic measurements. Hansen, P. A. 
As. Nr. 9 (1831) 189-, 237-. 

legal subjects. Jerwood, J. Devon. 
As. T. 2 (pt. 2) (1868) 578-. 

natural philosophy. La Place, P. S. 

(Marquis) de. Con. des Temps (1818) 
361-. 

petrography. Cesaro, G. Brux. Ac. 
Mm. 53 (1895-98) (No. 1) 55 pp. 

, practical. Littrow, J. J. von. Baum- 
gartner Z. 9 (1831) 433-. 

to science of humanity. Quetelet, L. A. J. 
Brux. Ac. Bll. 36 (1873) 19-. 

variations in the transparency of air. 
Seidel, L. Miinch. Sb. 2 (1863) 320-. 

average deviations. Hardy, G. F. I. Act. J. 

27 (1889) 214-. 
and averages, theory. Nekrasov, P. A. Bee. 

Mth. (Moscou) 21 (1901) 579-. 
correction of a formula. Laquiere, E. M. 

Par. S. Mth. Bll. 8 (1880) 74-. 
criticism of Laplace. Ruffini, P. Pisa N. G. 

1 (1822) 201-. 
definitions and principles of calculus of. 

Gosieicski, W. Wiad. Mt. 4 (1900) 137- ; 

Fschr. Mth. (1900) 230. 
demonstration of Gauss, rigour of a. Bertrand, 

J. C. B. 106 (1888) 563-. 
drawing lots. Jouffret, E. Bv. Mar. 38 (1873) 

5-, 523-, 957-. 
errors of calculations performed in duplicate. 

Glaisher, J. W. L. (vn) [1873] Mess. Mth. 3 

(1874) 106- . 
events which seldom happen, their possible 

frequency being unlimited. Seidel, P. L. von. 

Miinch. Ak. Sb. 6 (1876) 44-. 
experiments. Baker, A. Cn. I. P. 5 (1888) 

194-. 
gaming, with application to definite integrals. 

Mayer, D. E. Par. EC. Pol. J. 3 (1897) 

153-. 
general theorem, elementary proof. Tchebiclieff, 

P. Crelle J. 33 (1846] 259-. 
generalisation of a problem in. Azzarelli, M. 

Em. N. Line. At. 45 (1892) 72-. 
integration of recurring series. Ocagne, M. d'. 

Par. S. Mth. Bll. 15 (1887) 143-. 
judgments. Bertrand, J. Par. S. Phlm. Mm. 

Cent. (1888) 69-. 

in courts of appeal. Guibert, A. C. B. 7 
(1838) 650-. 

, especially in criminal cases. Poisson, S. D. 
C. B. 1 (1835) 473-. 

and evidence. Bienayme, J. Par. S. Phlm. 
PV. (1838) 93-. 

judicial errors. Ostrogradsky, M. A. St. Pet. 

Ac. Sc. Mm. 3 (1838) (Bll. Sc.) xix-. 
juries' verdicts. Coste, L. M. P. Liouv. J. 

Mth. 7 (1842) 169-. 

, proportion of condemnations. Poisson, 
S. D. C. B. 5 (1837) 355-, 459-. 



UNIVERSITY OF CALIFORNIA^ 
JBANTA JBAftBARA COLLEGE LIBRAE^ 

Probabilities: Problems 1630 

legal, decisions of majorities. Guibert, A. 

Liouv. J. Mth. 3 (1838) 25-. 
losses in war. Bouniakowsky, V. [1846] St. 

Pet. Ac. Sc. Mm. 6 (Pt. 1) (1850) 233-. 
. Lafrogne, (le It.) H. Bv. Mar. et 

Col. 142 (1899) 275-. 
principle, new. Bienayme, J. Par. S. Phlm. 

PV. (1840) 37-. 
, . Catalan, E. C. Brux. Ac. Bll. 44 

(1877) 463-; 8 (1884) 72-. 



Probabilities : Problems. 

Plana, G. Turin Mm. Ac. (1811-12) 355-. 
Rangoni, L. (xi) Mod. S. It. Mm. 18 (Mt.) 

(1820) 518-. 
Nieuport, C. F. F. de. Brux. Ac. Sc. Mm. 3 

(1826) 143-. 
Lubbock, J. W. [1828] Camb. Ph. S. T. 3 

(1830) 141-. 
Bernard, . Par. EC. Pol. J. 15 (cah. 24) 

(1835) 264-. 
Catalan, E. C. Liouv. J. Mth. 2 (1837) 469-; 

6 (1841) 75-. 

Levy, A. N. A. Mth. 1 (1842) 179-. 
Ostrogradsky, M. A. [1846] St Pet. Ac. Sc. 

Bll. 6 (1848) 321-. 

Terquem, 0. N. A. Mth. 5 (1846) 218-, 260. 
Dedekind, R. Crelle J. 50 (1855) 268-. 
Lazarus, W. I. Act. J. 15 (* 1870) 245-. 
Sutton, W. I. Act. J. 15 (*1870) 452-; 16 

(*1872) 151-. 

Lemoine, E. (x) Par. S. Mth. Bll. 1 (1873) 39-. 
Halphen, G. H. (x) Par. S. Mth. Bll. 1 (1873) 

221-. 
Jordan, C. (x) Par. S. Mth. Bll. 1 (1873) 

256-, 281-. 

Bienayme, J. Par. S. Mth. Bll. 2 (1874) 153-. 
Levdnen, S. Helsingf. Ofv. 17 (1875) 112-. 
Hoppe, R. Arch. Mth. Ps. 61 (1877) 410-. 
Bianco, 0. Z. G. Mt. 16 (1878) 169-. 
Woolhouse, W. S. B. I. Act. J. 21 (*1879) 

204-. 

Lemoine, E. As. Fr. C. B. (1880) 183-. 
Cesaro, E. (xn) Mathesis 2 (1882) 177-, 

232; 3 (1883) 233-. 
Gosiewski, W. (xn) [1882] Krk. Ak. (Mt.- 

Prz.) Bz. & Sp. 10 (1883) 137-, liii-. 
Lemoine, E. N. A. Mth. 3 (1884) 118- ; As. 



Fr. C. B. (1885) (Pt. 2) 50-. 
. Mg. 22 
Weill, . Par. S. Mth. Bll. 14 (1886) 158-. 



Edgeworth, F. Y. Ph. 



22 (1886) 371-. 



Cesaro, E. Palermo Cir. Mt. Ed. 1 (1887) 

299-. 

Mayer, E. C. B. 108 (1889) 391-. 
Pdnek, A. Casopis 20 (1891) 105- ; Fschr. 

Mth. (1891) 232. 

Makeham, W. M. I. Act. J. 29 (1892) 475-. 
Lemoine, E. As. Fr. C. B. (1895) (Pt. 1) 182. 
Lindelof, L. Helsingf. Ofv. 42 (1900) 79-. 
Hermite, C. Helsingf. Ofv. 42 (1900) 88-. 
analytical. Schlomilch, 0. Grunert Arch. 9 

(1847) 372-. 
Bernoulli, etc. Malfatti, G. F. Verona S. It. 

Mm. 1 (1782) 768-. 



101 



1630 Probabilities: Problems 

Bernoulli and Lagrange. Abbati, P. (viAdds.) 

Mod. Mm. S. It. 19 (1821) 385-. 
Bertrand, generalisation. Barbier, E. C. E. 

105 (1887) 407. 
, solution. Andr6, D. C. E. 105 (1887) 

436-. 

cards. Cantor, M. Schlomilch Z. 2 (1857) 410-. 
class. Sylvester, J. J. B. A. Ep. 35 (1865) 

(Sect.) 8-. 
collimator for adjustment of azimuth circle. 

Airy, G. B. B. A. Ep. (1850) (pt. 2) 1-. 
competitive examinations. Edgeworth, F. Y. 

Ph. Mg. 30 (1890) 171-. 
conditions limiting solution. Boole, (?. Ph. 

Mg. 8 (1854) 91-. 
election. Korteweg, D. J. N. Arch. Wisk. 1 

(*1875) 157- ; 2 (*1876) 40-. 
evidence. Doolittle, M. H. Wash. Ph. S. Bll. 

11 (1892) 602. 
game of pool. Arcais, F. d'. Padova Ac. 

At. e Mm. 16 (1900) 219-. 
graphic solution. Favaro, A. Yen. I. At. 3 

(1877) 1025-. 
Laurent. Pdnek, A. Casopis 20 (1891) 94-; 

Fschr. Mth. (1891) 231. 
note. Laquiere, E. M. Par. S. Mth. Bll. 8 

(1880) 79-. 
and relative values of pieces in game of chess. 

Lemoine, E. As. Fr. C. E. (1880) 179-. 
solution. Plana, G. Mod. S. It. Mm. 18 

(1818) 31-. 
. Brashmann, N. D. (xn) Mosc. Un. Mm. 

10 (1835) 523-. 
. Poisson, S. D. Liouv. J. Mth. 2 (1837) 

373-. 

. Hansen, P. A. As. Nr. 16 (1839) 9-, 27-. 
. Meyer, A. Brux. Ac. Bll. 15 (1848) (pte. 

2) 508. 

. Roger, E. Liouv. J. Mth. 17 (1852) 202-. 
. Blazejarski, E. N. A. Mth. 1 (1862) 131-. 
. Liagre, J. B. J. Brux. Ac. Bll. 17 (1864) 

365-. 
. Terrier, (Prof.) . Neuch. Bll. 9 (1873) 

. Hendricks, J. E. Des Moines Anal 3 

(1876) 152-. 

. Spitzer, S. D. Nf. B. (*1877) 97-. 
. Piuma, C. M. G. Mt. 17 (1879) 360-. 
. Spitzer, S. Arch. Mth. Ps. 64 (1879) 74-. 
. Bertrand, J. C. E. 105 (1887) 369, 437-. 
, application of. Poreckij, P. S. Kazan S. 

Nt. (Ps-Mth.) P. 5 (1887) 83- ; Fschr. Mth. 
(1887) 200. 
, geometrical. Lemoine, E. [18821 Par 

S. Mth. Bll. 11 (1883) 13-. 
solved by Poisson, indeterminateness. Bertrand 

J. C. E. 106 (1888) 636-. 
and theorems. Catalan, E. Brux. Ac. Mm. 

46 (1886) (No. 2) 16 pp. 
two. Andrade, . C. E. 130 (1900) 395-. 



Probabilities, etc. 1630 

repeated trials. Bertrand, J. C. E. 94 (1882) 

185- ; 105(1887) 1201-. 
subjective, mathematical and objective. 

Vassilief, A. [1900] N. Y. Am. Mth. S. 

Bll. 7 (1901) 158, 183. 
the surprise ratio. Bostwick, A. E. Science 3 

(1896) 66-. 
theorem. Luchterhandt, A . E. Grunert Arch. 

2 (1842) 65-. 

. Dienger, J. Prag Ab. 5 (1872) 44 pp. 

. De Forest, E. L. Des Moines Anal. 7 
(1880) 169-. 

. Bertrand, J. C. E. 114 (1892) 701-. 

of Bienayme, elementary proof. Bertrand, 
J. C. E. 81 (1875) 458, 491-. 

, demonstration. Wythoff, W. A, N. Ts. 
Mth. 4 (B) (1893) 77-. 

, new. Simmons, (Rev.) T. C. L. Mth. S. 
P. 26 (1895) 290-. 

, , application. Bienayme, J. C. E. 81 
(1875) 417-. 

theorems. Franklin, F. (xn) [1881] J. H. 
Un.^Cir. [1] (1882) 128. 

. Cebysev, P. St Pet. Ac. Sc. Mm. (Rs.) 
55 (1887) (Suppl.) No. 6, 16 pp. ; Acta Mth. 
14 (1890-91) 305-. 

"Theorie Analytique" (Laplace). Glaisher, 
J. W. L. [1872] Mess. Mth. 2 (1873) 62-. 

-- (-). Laurent, H. N. A. Mth. 12 
(1873) 176-. 

-- ( ). Tychsen, C. Kjob. Ov. (1876) 12-. 

theory. Encontre, D. Mntp. Eec. Bll. 1 
(1803) 9-. 

. Bellavitis, G. Poligrafo 4 (1836) 3-. 

. De Morgan, A. [1837] Camb. Ph. S. T. 
6 (1838) 423-. 

. Ellis, E. L. Camb. Mth. J. 4 (1845) 127-. 

. Boole, G. Camb. and Dubl. Mth. J. 6 
(1851) 286. 

. Donkin, W. F. Ph. Mg. 1 (1851) 353-, 
458-; 2 (1851) 55-. 

. Boole, G. Ph. Mg. 2 (1851) 96- ; 7 (1854) 
29-; 9 (1855) 165-. 

. Bellavitis, G. Yen. At. (1856-57) 299-. 

. Newcomb, S. Am. Ac. P. 4 (1857-60) 
433-; Camb. (M.) Mth. M. 1 (1859) 136-, 
233-, 331- ; 2 (1860) 134-, 272-; 3 (1861) 
119-, 343-. 

. Boole, G. Phil. Trans. (1862) 225-. 

. Plrogov, N. N. Es. Ps.-C. S. J. 19 
(Ps.) (1887) 19-. 

. Lindsay, T. Pop. As. 4 (1897) 240-. 

, and application to gunnery. Sabudski, N. 
Fschr. Mth. (1898) 197-. 

and applications. Czuber, E. D. Mth. Vr. 
Jbr. 7 (1899) (Heft 2) viii + 279 pp. 

evidence. De Morgan, A. [1846-50] 
Camb. Ph. S. T. 8 (1849) 379-; 9 (1856) 
79-. 

Ellis, E. L. [1842] Camb. 



Boole, G. Ph. Mg. 8 



question treated by d'Alembert. Maupin, G. 

Par. S. Mth. Bll. 23 (1895) 185-. 
Delannoy, . Par. S. Mth. Bll. 

23 (1895) 262-. 



, foundations. 

Ph. S. T. 8 (1 
, general me 

(1854) 431-. 
, geometrical, interpretation of 0. Simmons, 

(Rev.) T. C. As. Fr. C. E. (1893) (Pt. 1) 

175. 
, , problems. Vivanti, G. Ev. Mt. 1 

(1891) 69-. 



102 



1630 



Probabilities, Theory of Errors 



1630 



theory and practice. Wolf, R. Bern Mt. 

(1849) 97-, 183- ; (1850) 85-, 209- ; (1851) 

17- ; (1853) 25-. 
, principle. Young, J. R. B. A. Ep. (1844) 

(ft. 2) 1-. 
, proposition. Liapounoff, A. St Pet. Ac. 

Sc. Bll. 13 (1900) 359-. 

. Protection by mimicry. Blakiston, T., & 
'Alexander, T. Nt. 29 (1884) 405-. 
, two multiple integrals in. Czuber, E. 

Mh. Mth. Ps. 2 (1891) 119-. 

Probability of being hit by a projectile. Keller, 
0. A. Mines 19 (1891) 622-. 

and certainty, nature and limits. Miller, G. 
[1793] Ir. Ac. T. 5, 199-. 

of composite events. Simmons, (Rev.) T. C. 
As. Fr. C. E. (1896) (Pt. 2) 1-. 

. Delannoy, H. Par. S. Mth. Bll. 

26 (1898) 64-. 

curve, asymmetrical. De Forest, E. L. 
Des Moines Anal. 9 (1882) 135-, 161- ; 10 
(1883) 1-, 67-. 

, . Edgeworth, F. Y. Ph. Mg. 41 

(1896) 90-. 

of error of observation. Schlomilch, 0. Z. 
Mth. Ps. 17 (1872) 87-. 

in result of a certain computation. 
Franklin, F. (xn) [1881] J. H. Un. Cir. 
[1] (1882) 165. 

writing a series of numbers. 
Nipher, F. E. Am. J. Sc. 12 (1876) 79-. 

errors arising from uncertainty of last 

Z" re. Glaisher, J. W. . (vn) [1873] 
s. Mth. 3 (1874) 59-. 
, elementary proofs of laws. Laquiere, 

E. M. Par. S. Mth. Bll. 9 (1881) 69-. 
, law. Petitcol, (Capt.) . N. A. 

Mth. 4 (1885) 441- ; Ev. Mar. et Col. 91 

(1886) 70-. 
.,.--, Ocagne, M. d\ Par. S. Phlm. 

Bll. 6 (1894) (C. .R. No. 9) 2-. 
, . Gosieicski, W. Prace Mt.-Fiz. 9 

(1898) 117- ; Fschr. Mth. (1898) 186-. 
of observations. Cauchy, A. L. C. 

E. 37 (1853) 264-. 
position. Reina, V. Em. E. Ac. 

Line. Ed. 6 (1897) (Sent. 1) 107-. 

in sum or mean of observations. 
Jullien, (le pere) M. Tortolini A. 1 (1858) 
76-, 149-, 227-. 

, exact and popular estimates, comparison. 
Terrot, C. H. Edinb. E. S. P. 2 (1851) 228-. 

of finding isolated shoals. Littlehales, G. W. 
A. Mth. 9 (1894-95) 163-. 

, formulae. Jordan, C. C. E. 65 (1867) 
993-. 

of hitting a target. Merriman, M. [1897] 
N. Y. Am. Mth. S. Bll. 4 (1898) 88, 91-. 

, local. Crofton, M. W. [1867] L. Mth. S. 

P. 2 (1869) 54-. 
, , applied to straight lines drawn at 

random in a plane, and to proofs of theorems 

in integral calculus. Crofton, M. W. Phil. 

Trans. 158 (1868) 181-. 
, , proof of theorem. Heutnann, C. N. 

Ts. Mth. 4 (B) (1893) 25-; Fschr. Mth. 

(1893-94) 343. 



Probability, local, question in. Berg, F. J. 

van den. N. Arch. Wisk. 9 (*1882) 32-; 

10 (1884) 202. 
, , theorem of Crofton. Cavallin, C. B. S. 

Ts. Mth. 2 (1884) 1-; Fschr. Mth. (1884) 

181. 

that marriage of man over forty will be 
fruitful. Sprague, T. B. [1879] Edinb. E. 
S. P. 10 (1880) 202-. 

of means. Poisson, S. D. Con. des Temps 
(1827) 273- ; (1832) 3-. 

. Lobatscheivsky, N. Crelle J. 24 

(1842) 164-. 
. Lobatto, R. Arch. Wisk. Gn. 2 

(1860-63) 96-. 
, Laplace's rule. Bienayme, J. Par. 

Mm. Sav. Etr. 5 (1838) 513- ; Par. S. Phlm. 

PV. (1839) 42-; (1840) 19-. 
, Poisson generalised. Hauber, C. F. 

Baumgartner Z. 7 (1830) 406-. 

that n-gon can be formed from n parts of 
straight line. Berg, F. J. van den. N. Arch. 
Wisk. 18 (1891) 63-; Fschr. Mth. (1891) 
234. 

, physical basis. Edgeworth, F. Y. Ph. Mg. 
16 (1883) 433-. 

of system of errors, law of. Gosiewski, W. 
Prace Mt.-Fiz. 3 (1892) 33-; Fschr. Mth. 
(1892) 206- . 

that two numbers are relatively prime. 
Cesdro,E.- (xn) J. H. Un. Cir. [2] (1883) 85. 

Probable error, comparison of two values. 

LUroth, J. As. Nr. 87 (1876) 209-. 
of constants. Hagen, G. H. L. Berl. 

Ak. Sb. (1883) 1169-. 
, determination. Lilroth, J. As. Nr. 73 

(1869) 187-. 
, . Jordan, W. As. Nr. 74 (1869) 

209-. 
, (Jordan). Andres, C. G. G. As. Nr. 

74 (1869) 283-. 
, from differences of m equally exact 

observations. Andrts, C. C. G. As. Nr. 79 

(1872) 257-. 
, experimental determination of constant. 

Adcock, R. J. Des Moines Anal. 7 (1880) 

189. 
, Peter's formula. Helmert, F. R. As. 

Nr. 88 (1876) 113-. 
, . Johnson, W. W. N. Y. Mth. S. 

Bll. 2 (1893) 57-. 

of a series of observations. Guyou, E. 
C. E. 106 (1888) 1282-. 

, calculation. Mees, R. A . 

Z. Mth. Ps. 20 (1875) 145- ; 21 (1876) 126-. 
from sum of variations. Fechner, G. T. 

A. Ps. C. Jubelbd. (1874) 66-. 

errors, limit, in observations. Cesaris, 
G. A. de. Mil. Effem. As. (1811) 102-. 

inference. Terrot, C. A. Edinb. E. S. P. 
2 (1851) 288-. 

intersection of non-concurrent lines, geo- 
metrical determination of point of. Ocagne, 
M. d\ Par. EC. Pol. J. 63 (1893) 1-. 

value of least errors in a series of observa- 
tions. Bertrand, J. C. E. 106 (1888) 786-. 



103 



1630 Probabilities, etc. 

Probable value of a series of observations, 
mechanical representation. Newcomb, S. 
As. S. M. Not. 33 (1873) 573. 

values of constants in u=a+by. Anon. 
's Gravenh. I. Ing. Ts. (1884-85) (Verg.) 
68-. 

Random scattering of points on a surface. 

Kleiber, J. Ph. Mg. 24 (1887) 439-. 
Beckoning of chances (reproduction of 16th 

century work by Benedict Spinoza). Bier ens 

de Haan, D. N. Arch. Wisk. 11 (1884) 75-. 
Eeduction of observation equations in more 

than one observed quantity. Kummell, C. H. 

Des Moines Anal. 6 (1879) 97-. 
results of experiments. Lupton, S. Ph. 

Mg. 31 (1891) 418-. 
, criticism. Lupton's method. 

Pickering, S. U. Ph. Mg. 32 (1891) 90-. 
, objections raised to Pickering's 

method. Hayes, E. H. Ph. Mg. 32 (1891) 

99-. 
Eesolution of equations given by method of 

least squares in a particular case. Port, A. 

C. E. 105 (1887) 491-. 

Eestricted number of observations, interpreta- 
tion. Vallier, E. C. K. 128 (1899) 654-. 
, . Hatt, . G. K. 128 (1899) 

893-. 
Eesultant error, law. Schols, C. M. Delft EC. 

Pol. A. 3 (1887) 140-. 

Boots of the equation e** -^ (R-&) - 0. Markoff, 

A. St Pet. Ac. Sc. Bll. 9 (1898) 435-. 
Scoring at rifle matches. Mallock, A. Nt. 60 

(1899) 366-. 
. Burbury, S. H. Nt. 60 (1899) 

412. 

. Mallock, A. Nt. 60 (1899) 412. 

Speculation, theory. Bachelier, L. Par. EC. 

Norm. A. 17 (1900) 21-. 
Stationary motion in an infinite system of 

molecules. Burbury, S. H. L. Mth. S. P. 

29 (1898) 225-. 
Stock-exchange, probabilities connected with. 

Dormoy, E. As. Fr. C. E. (1886) (Pt. 1) 

79-; (1887) (Pt. 2) 214-. 
Success of prediction, measure of. Peirce, C. S. 

Science 4 (1884) 453-. 
Sum of least variations, estimation and utility. 

Fechner, G. T. [1874] Leip. Mth. Ps. Ab. 

11 (1878) 1-. 
Surveying, possible error in determination of 

a point. Soulages, E. Arg. S. Ci. A. 44 

(1897) 306-. 

with usual instruments, judging error in. 
Weisbach, J. Baumgartner Z. 4 (1837) 24-. 

Tables of numbers, error due to omitted decimal 
places. Frischauf, J. Z. Mth. Ps. 16 (1871) 
178-. 

Target, firing at. Bertrand, J. C. B. 107 
(1888) 205-. 

questions, probability applied to. Bertrand, J. 
C. B. 106 (1888) 232-, 387-, 521-. 

, . Jung, G. C. E. 106 (1888) 

1001-. 
Testimonies or judgments, combination. Boole, 

G. Edinb. E. S. T. 21 (1857) 597-. 



Actuarial Mathematics 1635 

Testimony and arguments. Abbott, (Rev.) T. K. 
Ph. Mg. 28 (1864) 12-. 

for facts contrary to analogy. Young, M. 
[1798] Ir. Ac. T. 7 (1800) 79-. 

, formulae for value. Bonicelli,P. (viAdds.) 
Majocchi A. Fis. C. 12 (1843) 167-. 

in legal cases, measure of force. Tozer, J. 
[1843] Camb. Ph. S. T. 8 (1849) 143-. 

Todhunter's History of Theory of Probability, 
passages. Bianco, O. Z. [1877] G. Mt. 16 
(1878) 26-. 

Tradition and probability. Macfarlane, A. 
I. Act. J. 22 (*1881) 356-. 

Transit observation, frequency of occurrence 
of each digit in lOths of seconds in chrono- 
graph observations. Eastman, J. R. [1873] 
Wash. Ph. S. Bll. 1 (1874) 85-. 

Triangulation, interpolation of a point by 
method of least squares. Jordan, W. Z. 
Mth. Ps. 16 (1871) 164-. 

Trigonometric measures, mean error of results. 
Borsch, (Dr) [A.] Arch. Mth. Ps. 46 (1866) 
40-. 

problem, surveying. Gauss, C. F. As. Nr. 
1 (1823) 81-. 

surveys, combination of errors in connexion 
with. Kriiger, L. Gott. Nr. (1900) 1-. 

Variability of organs, and Gauss's law of devia- 
tion. Ludwig, F. Z. Mth. Ps. 43 (1898) 
230-. 

Verification of predictions. Doolittle, M. H. 
Smiths. Misc. Col. 33 (1888) Art. 2, 122-. 
(Wash. Ph. S. Bll. 7 (1885).) 

Weighing of errors, theorems. Paucker, M. G. 
von. Mitau Arb. Kurland. Gs. 9 (1851) 141-. 

Weight of observations where mean of squares 
of errors is composed of several parts. Hel- 
mert, F. R. As. Nr. 89 (1877) 225-, 241-. 

and precision of an observation. Bertrand, J. 
C. E. 105 (1887) 1099-. 

Weighted causes, and Bessel's method. Paucker, 
M. G. Mitau Arb. Kurland. Gs. 9 (1851) 
170-. 



1635 Theory of statistics. 
Actuarial mathematics. 

Accident assurance, and connected questions. 

Tiselius, H. Stockh. Ofv. (1895) 561-. 
Accumulations of capital in United Kingdom, 

in 1875-85. Gi/en, R. Nt. 41 (1890) 

211-. 
Actuarial science, application of mathematics. 

Stuckey, J. J. Aust. As. Ep. (1893) 280-. 
Adjustment of mortality tables. Lazarus, W. 

I. Act. J. 16 (* 1872) 424-. 
. Woolhouse, W. S. B. I. Act. J. 

21 (* 1879) 37-, 56-. 
. Higham, J. A. I. Act. J. 23 

(*1882) 335-; 24 (1884) 44-. 
, Corneille and Landre's method. 

Danielewicz, B. Wiad. Mt. 1 (1897) 92-. 
, Gompertz's method. Gray, P. 

Assur. Mg. 7 ('1858)121-. 
, graphic method. Sprague, T. B. 

I. Act. J. 26 (1887) 77-. 



104 



Theory of Statistics. Actuarial Mathematics 



1635 



Adjustment of mortality tables, graphic me- 
thod. Woolhouse, W. S. B. I. Act. J. 26 
(1887) 420-. 

, method. M. Assur. Mg. 6 
(*1857) 357-. 

, . Woolhouse, W. S. B. I. Act. 

J. 29 (1892) 236-. 
, new method. Woolhouse, W. S. B. 

I. Act. J. 15 (*1870) 389-. 

, and weight of observations. 
McCay, C. F. I. Act. J. 22 (*1881) 24-. 

tables, Galloway's method. Watkins, C. 

Assur. Mg. 6 (*1857) 178, 360. 
, Woolhouse's formula. Higham, C. D. 

I. Act. J. 26 (1887) 50-. 
Age of parents as influencing sex and number 

of children. Brown, S. Assur. Mg. 3 (* 1853) 

17-. 
Ages at which life assurance is effected. 

Chandler, S. C. (jun.). I. Act. J. 17 

(*1873) 56-. 
Algebra of commercial exchanges. Cossali, P. 

[1812] Mod. Mm. S. It. 16 (1813) 124-. 
Allowance during sickness, tables. Higham, 

J. A. Assur. Mg. 7 (*1858) 112-. 
American life, law of. Nichols, W. S. I. Act. 

J. 19 (* 1876) 28-. 
Amount assured, and sum reserved, connection 

between. Jellicoe, C. Assur. Mg. 5 (* 1855) 

100-. 

of 1 for fraction of a year. Farren, E. J. 
Assur. Mg. 3 (*1853) 335-. 

. Chisholm, D. Assur. 

Mg. 3 (* 1853) 336-. 
. Filipowski, H. 

Assur. Mg. 3 (*1853) 338-; 4 (1854) 243-, 

253. 

and present value of regularly increasing 
annuity, formulae. Shaw, C. G. Assur. Mg. 
5 (*1855) 152. 

or decreasing annuities, 

formulae. Galsworthy, E. H. Assur. Mg. 5 

(*1855) 53-. 
Annual premium for life assurance. Gray, P. 

Assur. Mg. 2 (* 1852) 95-. 
term assurance on two joint lives. 

Sprague, T. B. Assur. Mg. 8 (*1860) 59-. 

and single payments, table connecting. 
Smith, H. A. Assur. Mg. 11 (*1864) 176-. 

premiums for endowment assurance. 

Smith, H.A. I. Act. J. 22 (1881) 143-. 
. McDonald, J. I. Act. J. 

32 (1896) 447-. 
Annuities. Horner, W, G. Thomson A. Ph. 8 

(1816) 279-, 388-. 

. Huet, . N. A. Mth. 5 (1846) 346-. 
. Nievengloski, G. H. N. A. Mth. 6 (1847) 

8-. 
. -Dupain, J. C. N. A. Mth. 2 (1863) 

464-. 
. Guldberg, A. S. (xn) Sk. Nt. Mot. F. 

(1880) 194-. 

. Bryan, G. H. Mth. Gz. 1 (1900) 8-. 
. Loney, . Mth. Gz. 1 (1900) 38-. 
, approximate calculation. Lobatto, R. 

[1861] Amst. Vh. Ak. 10 (1864) 32 pp. 
, . Bmmiakowsky, V. [1877] St Pet. 

Ac. Sc. Bll. 24 (1878) 437-. 



1635 



Annuities, assurance, etc., approximate calcu- 
lation. Stamkart, F. J. Amst. Vs. Ak. 1 
(1866) (Ntk.) 95-. 

and assurances, improved theory. Wool- 
house, W. S. B. I. Act. J. 15 (1870) 95-; 
18 (*1875) 151-. 

, (Woolhouse's). Button, W. 

I. Act. J. 15 (*1870) 307-. 

, Milne's treatise, correction of error. 



Hoskins, H. I. Act. J. 17 (*1873) 192-. 

3. We. 
Mg. 36 (1850) 8-. 



on successive lives. Weddle, T. Ph. 



on assured lives, value. Berridge, G. W. 
I. Act. J. 19 (*1876) 351-. 

, calculation. Lubbock, J. W. [1828] Camb. 

Ph. S. T. 3 (1830) 141-. 
__, _. Wrede, F. J. [1869] Stockh. Ofv. 26 

(1870) 5-. 
, . Fagnart, E. Mathesis 16 (1896) 64-. 

under certain conditions, values. Hardy, P. 
Assur. Mg. [1 (* 1851)] 1 bis-. 

, certain determining amounts of continuous. 

Makeham, W. M. I. Act. J. 15 (*1870) 432-. 
Annuities-certain, rate of interest. Hardy, 

G. F. I. Act. J. 23 (*1882) 266-. 
, theory. Makeham, W. M. I. Act. J. 14 

(1869) 189-. 

, value. Orchard, W. Assur. Mg. 
[1 (*1851)] 100 big-. 

, formula. Hansen, C. N. Ts. Mth. 11 (A) 

(1900) 65-. 
, formulae in D. Jones's work. Macfadyen, 

J. E. Assur. Mg. 13 (* 1867) 200. 
, . McCuaig, C. Assur. Mg. 

13 (*1867) 251-. 

involving three lives, approximations. 
Hardy, G. F. I. Act. J. 23 (*1882) 274-. 

and life-assurance. Tychsen, C. (xn) Ts. 
Mth. 5 (1875) 49-, 97-. 

assurances and premiums, calculation 

of worth. Hultman, F. W. Ts. Mt. Fys. 2 
(1869) 63-, 113-, 209-. 

expectations. Landre, C. L. N. 
Arch. Wisk. 12 (1886) 174- ; Fschr. Mth. 
(1885) 194-. 

on lives. Willich, C. M. Assur. Mg. 7 
(*1858) 273-. 

on three joint lives, approximate values. 
Hardy, P. Assur. Mg. 3 (*1853) 330-. 

, four, five and six joint lives, tables. 

Shaw, C. G. Assur. Mg. 5 (*1855) 180-. 

on several lives. Quiquet, A. C. B. Ill 
(1890) 337-. 

for long terms, approximations. Brown, S. 
Assur. Mg. [1(* 1851)] 20-. 

, mean annual extinction in chief Portuguese 
offices. Silva, D. A. da. Lisb. J. Sc. Mth. 
1 (1868) 175-. 

payable half yearly or quarterly. Sprague, 
T. B. Assur. Mg. 13 (*1867) 188-, 201-, 
305-. 

m times a year. Hansen, C. N. Ts. 

Mth. 11 (B) (1900) 58-. 
, question. Lindelof, L. L. Acta Mth. 3 

(1883) 97-. 

and rate of interest, theorems for deter- 
mining. Benwell, J. B. Tilloch Ph. Mg. 
49 (1817) 179-. 



105 



1635 



Theory of Statistics. Actuarial Mathematics 



1635 



Annuities, tables, comparison. Lubbock, J. W. 

[1829] Camb. Ph. S. T. 3 (1830) 321-. 
, of present values. Bowditch, J. I. Am. 

Ac. Mm. 1 (1333) 73-. 
, theorems for determining. Benwell, J. B. 

[1816-17] Thomson A. Ph. 8 (1816) 119- ; 

Tilloch Ph. Mg. 48 (1816) 449-; 50 (1817) 

164- ; 51 (1818) 6-. 
, theory. Landre, C. L. N. Arch. Wisk. 15 

(1888) 1-; Fschr. Mth. (1888) 235-. 
Annuity, analytic formula and table. Benwell, 

J. B. Tilloch Ph. Mg. 57 (1821) 161-. 

and assurance formulas, reduction. Wool- 
house, W. S. B. I. Act. J. 17 (*1873) 171-. 

_ tables for three lives. Braid, W. 

Assur. Mg. 6 (*1857) 109, 115-. 

certain, approximation to rate of interest. 
McKenzie, D. J. McG. I. Act. J. 23 (*1882) 
405-. 

and life annuity, analogy between. 
King, G. I. Act. J. 20 (*1878) 435-. 

, . Ryan, G. H. I. Act. J. 

25 (1886) 443-. 

computation on Makeham's hypothesis. 
McClintock, E. I. Act. J. 18 (*1875) 242-. 

forborn, determination. Hardy, P. Assur. 
Mg. 7 (*1858) 1-. 

, Lubbock's formula for approximation. 

Sprague, T. B. I. Act. J. 18 (*1875) 305-. 
, market value. Wilding, R. I. Act. J. 22 

(*1881) 61-. 

problem, and Arbogast's development. De 
Morgan, A. Assur. Mg. 12 (* 1866) 206-. 

, old and new solutions. Gray, P. Assur. 

Mg. 13 (* 1867) 60. 

question. C., J. I. Act. J. 14 (*1869) 

at one rate deduced from that at another. 
Meikle, J. Assur. Mg. 3 ("1853) 325-. 

, rate of interest. Meikle, J. Assur. Mg. 5 

(*1855) 152-. 
, . De Morgan, A. Assur. Mg. 8 

(*1860) 61-. 
, . McLauchlan, J. J. I. Act. J. 18 

(*1875) 290-. 

tables, method of checking. De Morgan, A. 
Assur. Mg. 2 (*1852) 390-. 

on three lives, application of Gompertz's 
law. Woolhouse, W. S. B. Assur. Mg. 10 
(*1863) 121-. 

, note on Woolhouse's paper. De 

Morgan, A. Assur. Mg. 10 (*1863) 237-. 

-, rule for value. De Morgan, A. 

(vi Adds.) ' Ph. Mg. 15 (1839) 337-. 

value with final payment. Cherriman, J. B. 
I. Act. J. 21 (* 1879) 299-. 

Apportionable annuities. Sprague, T. B. 

Assur. Mg. 13 (*1867) 358-; 14 (*1869) 36-; 

15 (*1870) 244. 
Apportionment, problem in. Sprague, T. B. 

I. Act. J. 19 (*1876) 372-. 
Arbitrary rates of life premium. S., H. A. 

Assur. Mg. 6 (*1857) 297-. 
Association of electors by lot. Bertrand, J. 

C. B. 106 (1888) 17-. 
Assurance on adventure so as to cover interest. 

Mercator. [Pseudon.] (vi Adds.) Bost. Mm. 

Am. Ac. 1 (1785) 183-. 



Assurance, analytical theory. Fourier, J. B. J. 
A. C. 10 (1819) 177-. 

and annuities, formulas. Enestrom, G. 
Stockh. Ofv. (1894) 561- ; Fschr. Mth. 
(1893-94) 364-. 

in another's favour. Dienger, J. Arch. 
Mth. Ps. 42 (1864) 333-. 

of capital and income. Unferdinger, F. 
Grunert Arch. 26 (1856) 408-. 

in stock. Danielewicz, B. Wiad. Mt. 

2 (1898) 32-. 

companies, amalgamation. Jellicoe, C. 
Assur. Mg. 7 (*1858) 254-. 

, . Sprague, T. B. Assur. Mg. 7 
(*1858) 355-. 

, equitable transference of business 
between. Sprague, T. B. Assur. Mg. 7 
(*1868) 301-. 

company, testing solvency. Younger, S. 
Assur. Mg. 7 (*1858) 183-, 295-. 

, . S.,H. A. Assur. Mg. 7 (*1858) 

294, 353-. 

, comparison of actual with expected ex- 
periences. Low, G. M. I. Act. J. 18 
(*1875) 195-. 

on continent, progress. Brown, S. Assur. 
Mg. [1 (*1851)] 293-; 2 (* 1852) 16-. 

, demonstration of certain formulas. Adler, 

M. N. Assur. Mg. 12 (1866) 52-. 
, a fallacy concerning. Gray, P. I. Act. J. 

14 (*1869) 63-. 

of invalid lives. Younger, S. Assur. Mg. 
11 (*1864) 49-. 

, Younger's plan. Brabrook, E. W. 

Assur. Mg. 10 (*1863) 349-. 
, . Smith, H. A. Assur. Mg. 

10 (*1863) 352-; 11 (* 1864) 180. 
, . Gray, P. Assur. Mg. 10 

(*1863) 354-. 

against invalidity. Lazarus, W. I. Act. J. 

15 (*1870) 143-. 

and old age, German method. Young, 

T. E. I. Act. J. 29 (1892) 269-. 
issue. Tucker, R. Assur. Mg. 5 (*1855) 

350-. 
, premiums. Sprague, T. B. I. Act. 

J. 28 (1890) 350-. 
, rate of premium. Day, A. Assur. 

Mg. 8 (*1860) 127-. 
, life against life, value. Bailey, A. H. 

Assur. Mg. 9 (M861) 299. 
, , and for n years longer. Tucker, 

R. Assur. Mg. 4 (*1854) 250-. 
, , t years longer. CJiatham, J. 

I. Act. J. 25 (1886) 439-. 

loan (kind of life assurance). Vesz, J. A. 
(xn) Mag. Tud. Ak. Etk. (Mth.) [1] (No. 3) 
(1868) 20 pp. 

payable at instant of death. Younger, S. 
Assur. Mg. 7 (*1858) 238. 

pensions, theory. Enestrom, G. Stockh. 
Ofv. (1895) 197-, 243-; Fschr. Mth. (1895) 
249-, 250-. 

premiums on ill health. Danielewicz, B. 
Wiad. Mt. 1 (1897) 170-. 

of recently selected lives, premiums. Sprague, 
T.B. I. Act. J. 20 (* 1878) 95-. 



106 



Theory of Statistics. Actuarial Mathematics 



1635 



Assurance against sickness. Moser, C. Arch. 

Sc. Ps. Nt. 6 (1898) 364-. 
, some new forms. Fix, . Ev. Sc. 3 

(1895) 171- 
, state-loans, &c. Oettinger, L. Grunert 

Arch. 36 (1861) 189-, 453-; 37 (1861) 125-, 

365-; 38 (1862) 263-. 

of survivor, formula for premium. Lobatto, 
R. [1865] Arch. Neerl. 1 (1866) 46-. 

to survivor, new method of calculating. 
Reboul, E. Assur. Mg. 9 (*1861) 1-. 

of unsound lives, practice concerning. 
Humphreys, G. I. Act. J. 18 (*1875) 178-. 

for widows, theory. John, G. Jb. Berg- 
Hw. (1888) 42-. 

Auxiliary life contingency tables, history. 

Hendriks, F. Assur. Mg. [1 (*1851)] 1-, 

12 Ms-. 
Average duration of life. Merrifield, C. W. 

Assur. Mg. 6 (*1857) 175-. 
, calculation for Prussia. Dieterici, 

C. F. W. Berl. Ab. (1858) (Ph.) 433-. 

life office, determination of an. King, G. 
I. Act. J. 20 (*1878) 300-. 

mortality rates, groupings according to age. 
Gray, W. T. I. Act. J. 25 (1886) 369-. 

premium, theory. Harvey, C. J. I. Act. 
J. 24 (1884) 296-. 

prices, official ("mercuriali"). Pareto, E. 
(x) Em. E. Ac. Line. At. 26 (1873) 599-; 
1 (1875) 3-. 

Averages, and application to rate of exchange. 

Drobisch, M. W. Leip. B. 23 (1871) 25-. 
, general. Morrison, R. Assur. Mg. 12 

(*1866) 350- ; 13 (* 1867) 39-, 161-. 

and life contingencies, use of integral cal- 
culus. Younger, S. Assur. Mg. 7 (*1858) 
71-. 

, percentage of. Preece, W. H. (xi) Tel. 

E. J. 2 (1873) 293-. 

Bank-notes, mathematical theory of. Walras, 

L. [1879] Laus. S. Vd. Bll. 16 (1880) 553-. 

Banking, mathematical theory. Edgeworth, 

F. Y. B. A. Ep. (1886) 777-. 
Barrett's method and questions of nomen- 
clature. De Morgan, A. Assur. Mg. 10 
(*1863) 301-. 

Benefits, calculation of certain. Sprague, 
T. B. I. Act. J. 24 (1884) 327-. 

, complex, calculation. King, G. I. Act. J. 
26 (1887) 276-. 

paid several times a year and complete 
annuities. King, G. I. Act. J. 24 (1884) 
418-. 

, present or future, formula. Macfadyen, 

J. R. I. Act. J. 17 (*1873) 381-. 
Births and deaths at Brussels, laws. Quetelet, 

L. A. J. Brux. Ac. Sc. Mm. 3 (1826) 495-. 
in Hanau. Moller, (Dr) von. (vi 

Adds.) Wet. Gs. Jbr. (1861-63) 59-. 
, Stuttgart 1847. Cless, G. Wiirtb. 

Jh. 4 (1849) 120-. 
, deaths and marriages in Prussia, 1820- 

1834. Hoffmann, J. G. Berl. Ab. (1841) 

(Th. 3) 1-. 

of different sexes, effect of legitimacy on 
ratio. Prevost, P. Bb. Un. 42 (1829) 
139-. 



1635 



Births, proportion of girls and boys. Poisson, 
S. D. Par. Mm. Ac. Sc. 9 (1830) 239-. 

, statistics (Versailles). Berigny, A. Par. 
An. M6t. (1852) 281-. 

in various states of Europe and particularly 
Prussia. Dieterici, C. F. W. Berl. Ab. (1855) 
(Ph.) 321-. 

Bond bought at premium, rate of interest. 

Todhunter, R. I. Act. J. 33 (1898) 356-. 
Bonus distribution, system. Rothery, H. J. 

I. Act. J. 30 (1893) 131-. 
, theory. Andras, H. W. I. Act. J. 32 

(1896) 320-. 
Bonuses as affecting annuities. Macfadyen, 

J. R. I. Act. J. 14 (*1869) 364-. 
Building debts, discharge by capital or rent. 

Wittstein, T. Hann. Z. Archt.-Vr. 7 (1861) 

107-. 
Calculation in economics. Durini, G. N. 

[1834] Nap. At. I. Inc. 6 (1840) 1-. 
Cape of Good Hope Mutual Life Assurance 

Company, report. Sprague, T. B. I. Act. 

J. 20 (*1878) 358-. 
Carlisle and other tables, relations. Henry, J. 

Assur. Mg. 11 (* 1864) 89-, 
t . (Criticism of Henry's paper.) 

Farr, W. Assur. Mg. 11 (*1864) 109-. 

table of mortality, Milne's method in con- 
struction. Sutton, W. I. Act. J. 24 (1884) 
110-, 186-. 

Census. Lubbock, (Sir) J. W. (vi Adds.) 
Ph. Mg. 7 (1830) 416-. 

from 1801-1881, account of. Burridge, 
A. F. I. Act. J. 25 (1886) 83-. 

, principles of statistics applied. Hough, 
F. B. Am. As. P. 17 (1868) 145-. 

theorem, applications. Listing, J. B. Gott. 
Nr. (1867) 430-. 

Centenarians in France (census of 1886). 

Levasseur, E. C. E. 107 (1888) 71-. 
Chances, doctrine, and subdivision of risks. 

Young, Dr T. QJ. Sc. 22 (1827) 84-. 
Changes of population of Great Britain of 

various classes, 1811-1821. Harvey, G. 

QJ. Sc. 16 (1823) 203-. 
Chisholm's policy tables, method of using. 

McKenzie, D. J. McG. I. Act. J. 28 (1890) 

247-. 

tables, advantages. B., W. F. Assur. Mg. 
8 (*1860) 110-. 

Civil life, mathematics relating to. Michelsen, 

J. A. C. (vi Adds.) Berl. Sm. D. Ab. 3 

(1799) (Mth.) 36-. 
Claim acceleration reserve. Higham, C. D. 

I. Act. J. 24 (1884) 76; 26 (1887) 478. 
Classification of policies to obtain a table of 

mortality. Brown, S. Assur. Mg. 4 (* 1854) 

282-. ' 
Coinage ; introduction of decimal system. 

Farey, J. Tilloch Ph. Mg. 49 (1817) 15-. 

and money of account, subsidiary principle 
applied. Elliott, E. B. Am. As. P. 24 
(1875) 87-. 

, ternary denominational system, prerogative. 

Sylvester, J. J. (xii) [1881] J. H. Un. Cir. 

[1] (1882) 132. 
Coins, nomenclature, &c. Costaz, . [1831] 

Par. Mm. Ac. Sc. 12 (1833) 599-. 



107 



1635 



Theory of Statistics. Actuarial Mathematics 



Combined marriage and mortality table. 

Sprague, T. B. I. Act. J. 21 (*1879) 

406-. 
Commutation, or D and N, tables. Chisholm, 

J. I. Act. J. 14 (1869) 20Q-. 

formulae, certain. Smith, H. A. Assur. 
Mg. 8 (* 1860) 116- ; I. Act. J. 19 ( 1876) 
143. 

system, use of difference columns. Laundy, 
S.L. Assur. Mg. 8 ( 1860) 168-. 

tables of D. Chisholm. Meikle, J. Assur. 
Mg. 7 (* 1858) 297-. 

Complete annuities, formulas. Sheppard, H. N. 
I. Act. J. 32 (1896) 458-. 

annuity, formulae for purchase. Sorley, J. 
I. Act. J. 20 (* 1878) 454-. 

, market value. Baden, A. I. Act. J. 
17 (*1873) 447-. 

, . Carr, T. I. Act. J. 18 (* 1875) 

224-. 

payable by instalments, approximate 
value. Hoskins, H. I. Act. J. 19 (1876) 
143-. 

m equal instalments each year, 
value. Carr, T. I. Act. J. 18 (*1875) 
247-. 

Composition of decremental forces, theory. 
Makeham, W. M. I. Act. J. 18 (*1875) 
317-. 

for leave to reside abroad. Campbell, E. 
Assur. Mg. 9 (*1861) 167-. 

Compound survivorship annuity. Hardy, G. F. 
I. Act. J. 34 (1899) 93-. 

problem, solution. Makeham, W. M. 
Assur. Mg. 10 (*1863) 241-. 

Constancy of number of marriages and moral 

statistics. Quetelet, L. A. J. Brux. Ac. Bll. 

5 (1858) 89-. 
Constructive total loss, doctrine. Hopkins, M. 

Assur. Mg. [1 ( 1851)] 63-. 
Consumption in relation to life assurance. 

Lyon, T. G. I. Act. J. 30 (1893) 120- ; 

31 (1895) 155. 
Contingencies, distinct, problems involving. 

MakeMm, W.'M. Assur. Mg. 13 (*1867) 

109-. 
Contingent assurances, calculation. Colenso, 

F. E. I. Act. J. 32 (1896) 185-. 
with certain limitations. Otter, W. C. 

Assur. Mg. 7 (*1858) 239-. 
, premiums. Sunderland, A. W. I. Act. 

J. 26 (1887) 58-. 
, problem. Lidstone, G. J. I. Act. J. 

35 (1901) 480-. 

parts of terminable annuity. Gray, P. 
Assur. Mg. 11 (*1864) 172-. 

reversionary interests. Sang, E. Assur. 
Mg. [1 (*1851)] 18W-, 151-, 287-. 

. Jellicoe, C. Assur. Mg. 2 (*1852) 

. Tucker, JR. Assur. Mg. 5 (*1855) 
162, 239. 

reversions. Paterson, W. B. I. Act. J. 30 
(1893) 536-. 

Copyhold, enfranchisement, tables. Smyth, E, 
I. Act. J. 21 (*1879) 381-. 

fine enfranchisement. Mathews, G. S. I. 
Act. J. 28 (1890) 1-. 



1635 



Copyhold, fines payable on renewal, formulae. 

Ryley, E. Assur. Mg. 4 (* 1854) 367-. 
Corn-law sliding scale, expression for discon- 
tinuous law. Smith, Arch. Camb. Mth. 

J. 3 (1841) 152. 
Criminals, decay of morality in relation to 

number of youthful. Hoffmann, J. G. Berl. 

B. (1838) 1-. 
Cumulative vote. Langley, E. M. Mth. Gz. 

1 (1900) 160. 
Curves representing statistics. Edgeworth, F. 

Y. B. A. Ep. (1899) 825. 
D, N columns of a certain company. Morgan, 

W. Assur. Mg. 12 (*1866) 235-. 

and N formula for term assurance. Smith, 
H.A. I. Act. J. 19 (*1876) 143. 

Dacca census. Walters, H. As. Kesearches 

17 (1832) 534-. 
Date of death and payment, period between. 

Farren, E. J. Assur. Mg. 3 (*1853) 234-. 
Death strain in a life office, computation. 

Ryan, G. H. I. Act. J. 30 (1893) 196-. 
, true measure. Higham, C. D. I. Act. 

J. 20 ( 1878) 153-. 

Deaths, excess over births in coloured popula- 
tion of Boston. Boudin, J. C. M. F. J. C. 

B. 61 (1865) 746-. 
Debt, gradual discharge. Drobisch, M. W. 

Leip. B. 2 (1848) 1-. 
Decimal systems of money etc. Grubb, T. 

[1855] Dubl. E. S. J. 1 (1856-57) 21-. 
Decrement of human life, formula. Young, 

Dr T. Phil. Trans. (1826) (pt. 3) 281-. 
Deductions from sums assured, calculation. 

Hardy, G. F. I. Act. J. 32 (1896) 153-. 
Deferred annuities, tables. Stephenson, J. W. 

Assur. Mg. 12 (*1866) 178- ; 13 (1867) 

assurances and premiums. Rothery, H. J. 
I. Act. J. 28 (1890) 483-. 

and other life annuities, approximation. 
Ivory, H. Assur. Mg. 4 (*1854) 29 1-. 

De Moivre's formula. Gray, P. Assur. Mg. 

12 (*1866) 232-. 
, method of obtaining. Charlon, . 

I. Act. J. 15 (*1870) 141-. 
Deterioration, estimating increase of rate to 

meet. Smith, H. A. Assur. Mg. 10 (*1863) 

120. 
Determination of present value of mine on the 

Eand. Hellmann, F. I. Mn. Metall. T. 6 

(1898) 229-. 

Development and health, estimation from re- 
ports of recruiting officers. Bischoff, T. L. W. 

Munch. Sb. (1867) (I.) 282-. 
Dice for statistical experiments. Galton, F. 

Nt. 42 (1890) 13-. 
Differential tariffs. Courau, J. Arg. S. Ci. 

A. 50 (1900) 86-. 
Direct taxation, true measure of liability. 

Jellicoe, C. Assur. Mg. 3 (*1853) 1-. 
Discounted bonus premiums, rationale. Moir, 

H. I. Act. J. 36 (1902) 4-. 
Discounting of bills, mathematical theory. 

Necaev, N. V. Kazan S. Nt. (Ps.-Mth.) 

P. 3 (1885) 95-. 
, . Preobralenskij, V. V. Kazan 

S. Nt. (Ps.-Mth.) P. 3 (1885) 97-. 



108 



1635 



Theory of Statistics. Actuarial Mathematics 



1635 



Diseased lives, valuation reserve necessary. 

Sorley, J. I. Act. J. 20 (*1378) 342-. 
Dispositions of code of criminal instruction. 

Gergonne, J. D. Gergonne A. Mth. 9 (1818- 

19) 306-. 

Distribution by months of conceptions and 

births. Villerme,L. A. Sc. Nt. 24 (1831) 130-. 
, pure theory of. Berry, A. B. A. Ep. 

(1890) 923-. 
Doctrine of successive lives. Gray, P. Assur. 

Mg. 2 (*1852) 1-, 271-. 
Doctrines of political economy, mathematical 

exposition. Whewell, W. [1829-31] Camb. 

Ph. S. T. 3 (1830) 191- ; 4 (1833) 155-. 
population. Farr, W. B. A. Ep. (1877) 

(Sect.) 174-. 

Drummond's rule for calculating relative im- 
portance of boroughs, attempt to prove. 

M'Intyre, (Dr). (vi Adds.) Ph. Mg. 11 

(1832) 360-. 
Drunkenness in towns of England and Wales. 

Poynting, J. H. Manch. Lt. Ph. S. P. 16 

(1377) 211-. 
Economic science and statistics section of 

British Association, address. Duff, M. E. G. 

B. A. Ep. 37 (1867) (Sect.) 132-. 
, . Brown, S, B. A. 

Ep. 38 (1868) (Sect.) 144-. 
, . Northcote, (Sir) S. 

B. A. Ep. 39 (1869) (Sect.) 173-. 
, . Jevons, W. S. B. 

A. Ep. 40 (1870) (Sect.) 178-. 

, . Neaves, (Lord). 

B. A. Ep. 41 (1871) (Sect.) 191-. 
, . Fawcett, (Prof.) 

H. B. A. Ep. 42 (1872) (Sect.) 217-. 

, . Campbell, (Sir) G. 

B. A. Ep. (1876) (Sect.) 186-. 

utility of means of transport, especially 
railways. Perozzo, L. Em. E. Ac. Line. 
Mm. 1 (1894) 476-. 

Election methods. Nanson, E. J. [1882] Viet. 
E. S. T. 19 (1883) 197-. 

problem, to secure proportional representa- 
tion of parties. Phragmen, E. Stockh. Ofv. 
(1894) 133-. 

Elections, counting votes at general. Cauchy, 

A. L. C. E. 26 (1848) 469-. 
, multiple, theory. Phragmen, E. Stockh. 

Ofv. (1396) 181-. 

and representative system. Gergonne, J. D. 
Gergonne A. Mth. 6 (1315-16) 1-; 10 (1819- 

20) 281-. 

Electoral districts, problem. Thiele, T. N. N. 
Ts. Mth. 1 (B) (1890) 56-; Fschr. Mth. (1890) 
232-. 

, system; and the minority. Lorenz, L. 

N. Ts. Mth. 1 (B) (1890) 40-; Fschr. Mth. 
(1890) 232-. 

Endowment assurance, demonstration of for- 
mula. Sprague, T. B. Assur. Mg. 8 (*1360) 
111-. 

, easy method of calculating reserves. 
Weninger, V. (xn) Mag. Ak. Ets. (Mth. 
Term.) 6 (1365) 241-. 

, formula. M., A. Assur. Mg. [1 (*1851)] 



Endowment assurance policies. Sunderland, 

A.W. I. Act. J. 28 (1890) 257-. 
payable at ages 50, 55, 60, 65, tables. 

Garment, I). I. Act. J. 23 (*1882) 224-. 
, periodical valuation. Thomson, H. A 

I. Act. J. 34 (1899) 1-. 
, tables. Besant, A. D. I. Act. J. 31 

(1895) 366-. 

assurances, grouping for valuation. Alten- 
burger, J. I. Act. J. 34 (1899) 150- ; 35 
(1901) 332-. 

on two joint lives, approximate calcula- 
tion. Lidstone, G. J. I. Act. J. 33 (1898) 
354-. 

, valuation in groups. Lidstone, G. J. 
I. Act. J. 34 (1899) 61-, 510-. 

policies some time in force, valuation. 
Samot, D. J. A. I. Act. J. 20 (*1878) 
344-. 

value, deducing annuity and assurance 
value. Laundy,S.L. Assur. Mg. 11 (* 1864) 

Entailed estates, problem concerning. Sprague, 

T. B. I. Act. J. 19 (*1876) 38-. 
Equal partition in inheritance, effect of age 

difference. Mayette, J. Macon Ac. A. 6 

(1388) 360-. 
Equated time of payment. Levine, A. I. Act. 

J. 33 (1898) 539-. 
Equation of payments. Walton, W. Camb. 

Mth. J. 2 (1841) 188-. 
. Schulze, L. E. Grunert Arch. 36 

(1861) 177-. 
. (Malcolm's rule.) Benwell, J. B. 

Tilloch Ph. Mg. 49 (1817) 269-. 
Equitable Society's experience. Young, Dr T. 

Ph. Mg. 4 (1828) 339-. 
Estate duty. Lame, G. N. A. Mth. 7 (1848) 

360-. 
, mathematical law of progression. Lame, 

G. C. E. 27 (1848) 125-. 
, . Dienger, J. Grunert Arch. 

12 (1849) 401-. 
Exchange, mathematical theory. Walras, L. 

[1873] Laus. S. Vd. Bll. 12 (1874) 317-. 

value of money, mathematical theory. 
Vilfredo-Pareto, . As. Fr. C. E. (1894) 
(Pt. 2) 1180-. 

Expectation and estate. Westergaard, H. (xn) 

Ts. Mth. 6 (1876) 11-. 

Expected deaths and expected claims, estima- 
tion. Ryan, G. H. I. Act. J. 26 (1887) 

249-. 
Expenses of life assurance companies, measure. 

Macfadyen, J. E. I. Act. J. 19 (*1876) 153-, 

445-. 
, . Sprague, T. B. I. Act. J. 

19 (*1876) 167-, 305-, 447-. 
"Exposed to risk," new formula for deducing. 

King, G. I. Act. J. 27 (1889) 218-. 
Extra mortality. White, F. W., & Whittall, 

W. J. H. I. Act. J. 24 (1884) 385-. 

premium. Macfadyen, J. E. I. Act. J. 17 
(*1873) 77-. 

, conditional payments. Younger, S. 
Assur. Mg. 10 (*1863) 268-. 

for foreign climates. Meikle, J. I. Act. 

J. 19 (*1376) 268-. 



109 



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Theory of Statistics. Actuarial Mathematics 



1635 



Extra premiums on deteriorated lives, dispens- 
ing with. Hakeham, W. M. I. Act. J. 17 
(*1873) 153-. 

risk, data for fixing premiums. Jellieoe, C. 
Assur. Mg. 7 (*1868) 131-. 

risks, adjustment. Makeham, W. M, I. 
Act. J. 14 (*1869) 159-, 242-. 

, considered in relation to hypothetical 

table of mortality. Ryan, G. H. I. Act. J. 
24 (1884) 19-. 

owing to hereditary phthisis. Manly, 
H. W. I. Act. J. 30 (1893) 97-, 338-. 

. Macaulay, T. B. I. Act. 

J. 30 (1893) 335-. 
Facts, mode of tabulating, to show risks. 

Meikle, J. I. Act. J. 31 (1895) 229-. 
Family annuities. King, G. I. Act. J. 30 

(1893) 291-. 
Farr's healthy life table. Davis, W. Assur. 

Mg. 10 (*1863) 59-. 
Fatal accidents in various occupations. 

Whittall, W. J. H. I. Act. J. 23 (*1882) 

188-. 
Fecundity in Europe at beginning of nineteenth 

century. Benoiston de Chdteauneuf, . 

Par. Mm. Sav. Etr. 3 (1832) 608-. 
of marriages in interior of Cuba. La Sagra, 

E. de. C. E. 58 (1864) 524-. 
Female compared with male lives. Walford, 

C. I. Act. J. 19 (*1876) 174-. 
Females of British peerage, adjusted mortality 

table. Thiele, T. M. I. Act. J. 16 (*1872) 

43-, 118- . 
Finite differences calculus, and its applications. 

Otter, W. C. Assur. Mg. 7 (*1858) 333-; 

8 (*1860) 19-. 

Finlaison and English life table. Bailey, A. 

H. Assur. Mg. 9 (*1861) 357-. 
. Porter, H. W. Assur. Mg. 

10 (*1863) 31-. 
Finlaison 's report on mortality of government 

life annuitants. Porter, H. W. Assur. Mg. 

9 (*1861) 277-. 

tables. Smith, H. A. Assur. Mg. 13 
(*1867) 58-. 

Fire assurance. Barrois, T. Lille Mm. S. 

(1834) 85-. 
, apportionment of loss in. Miller, T. 

Assur. Mg. 6 (*1857) 202-. 
, divisions of risk in. Miller, T. Assur. 

Mg. 8 (*1860) 232-. 

in Great Britain. Brown, S. Assur. 
Mg. 7 (*1858) 259-, 341- ; 8 (*1860) 27-. 

, scientific application of data. Walford, 

C. I. Act. J. 21 (*1879) 1-. 
, specific and average. Miller, T. Assur. 

Mg. 8 (*1860) 140-. 
statistics. Miller, T. Assur. Mg. 6 

(*1857) 333-; I. Act. J. 22 (*1881) 103-. 

, settlement under average policies. 
Atkins, R. Assur. Mg. 3 (*1853) 147-. 

. . Lazarus, W. Assur. Mg. 

4 (*1854) 73-. 
. . Atkins, R. Assur. Mg. 

7 (*1858) 24-; 8 ('I860) 1-. 
, specific and average policies. 

Christie, D. Assur. Mg. 8 (*1860) 146-. 



Fires in London from 1833 to 1849. Broicn, S. 

Assur. Mg. [1 (*1851)] 31 bis. 
1856, causes. Fothergill, 

C. G. Assur. Mg. 7 (*1858) 91-. 
First and subsequent marriage in peerage. 

Day, A. Assur. Mg. 10 (*1863) 181-. 
Force of mortality, formula. De Forest, E. L. 

I. Act. J. 22 (*1881) 231-. 
, general expression. Sheppard, H. N. 

I. Act. J. 32 (1896) 295. 
, . Lidstone, G. J. I. Act. J. 

32 (1896) 390-. 
, Makeham's formula. Calderon, H. P. 

I. Act. J. 35 (1901) 157-. 
Foreign loans, rate of interest on, theory. 

Sutton, W. I. Act. J. 19 (*1876) 77-. 
Formula a x = vp (1 + a,,.^) and other matters. 

Gray, P. Assur. Mg. 12 (*1866) 176-. 
Foundlings, historical and statistical notice. 

Lepasquier, . Eouen Tr. Ac. (1830) 73-. 
French law, succession of illegitimate children. 

Cournot, A. A. (vi Adds.) Ferussac Bll. 

Sc. Mth. 16 (1831) 3-. 
, . Quillet, . N. A. Mth. 

4 (1845) 249-. 
Friendly societies, application of actuarial 

principles, &G. Hardy, G. F. I. Act. J. 

27 (1889) 245-. 
, experiences. Hardy, R. P. I. Act. J. 

31 (1895) 86-. 

, present position. Brown, S. Assur. 
Mg. 11 (*1864) 333-. 

, sickness and mortality experienced in. 

Tompkins, H. Assur. Mg. 5 (*1855) 6-. 

, tabulation of results. Watson, A. W. 
I. Act. J. 35 (1901) 268-. 

society levies. King, G. I. Act. J. 26 
(1887) 389-. 

. Hardy, G. F. I. Act. J. 26 (1887) 

478-. 
Fruitful marriages, probability. Sprague, T. 

B. I. Act. J. 25 (1886) 160-. 

, relative age of husband and wife. 
Chatham, J. I. Act. J. 27 (1889) 37-. 

Gain or loss from mortality in annuity company. 

Ryan, G. H. I. Act. J. 30 (1893) 189-. 
Geographic statistics, correction of anterior 

elements. Luca, F. de. Nap. Ed. 5 (1866) 

183-. 
Gold and silver, consumption in Britain 1810 

to 1829. Jacob, W. Edinb. N. Ph. J. 12 

(1832) 346-. 
Gompertz's formula, and application to duration 

of life. Simon, C. Bll. Sc. Mth. As. 2 

(1871) 282-. 

law. De Morgan, A. Assur. Mg. 8 (*1860) 
181- ; 9 (*1861) 214-. 

. Sprague, T. B. Assur. Mg. 9 (*1861) 

288-. 
. Govan, J. I. Act. J. 34 (1899) 147-. 

, consideration of alleged inaccuracies. 
Sprague, T. B. Assur. Mg. 10 (*1863) 32-. 

, exposition, new. Edmonds, T. R. 
Assur. Mg. 9 (*1861) 327-. 

, further development Makeham, W. M. 

I. Act. J. 28 (1890) 152-, 185-, 316-, 416. 

, Makeham's extension. Woolhouse, W. 
S. B. I. Act. J. 28 (1890) 481-. 



110 



1635 



Theory of Statistics. Actuarial Mathematics 



1635 



Gompertz's law, Makeham's modification, 
application. Colenso, F. E. I. Act. J. 31 
(1895) 337-. 

, value. Edmonds, T. R. Assur. Mg. 
10 (*1863) 104-. 

Gotha life assurance, mortality experience. 

Hopf, G. Assur. Mg. 5 (*1855) 324-; 6 

(*1857) 1-. 
Government annuity and assurance rates. 

Adler, M. N. Assur. Mg. 12 (*1866) 265-. 

life annuities. Adler, M. N. Assur. Mg. 
12 (*1866) 3-. 

Graduated mortality table from limited experi- 
ence. Chandler, S. C. (jun.). I. Act. J. 
17 (*1873) 161-. 

, graphic method. Lidstone, 

G. J. I. Act. J. 30 (1893) 212-. 

Graduation. Higham, J. A. I. Act. J. 31 
(1895) 319-. 

of experience, Jellicoe's formula. Suttcm, 
W. I. Act. J. 18 (*1875) 375-. 

formulae. Higham, J. A. I. Act. J. 27 
(1889) 427-. 

. Hardy, G. F. I. Act. J. 32 (1896) 

371-. 
, Higham's theory. Levine, A. I. Act. J. 

32 (1896) 290-. 

of mortality table, application of Makeham's 
method. Sorley, J. I. Act. J. 20 (*1878) 
340-. 

, methods. Button, W. I. Act. J. 

20 (*1878) 170-, 192-. 
tables. Sorley, J. I. Act. J. 22 

(*1881) 309-. 
. Ackland, T. G. I. Act. J. 23 

(*1882) 352-. 
. Higham, J. A. I. Act. J. 25 

(1886) 15-, 245-. 
, Makeham's law. King, G., & 

Hardy, G. F. I. Act. J. 22 (*1881) 191-. 
, . Sorley, J. I. Act. J. 22 

(*1881) 230-. 

, Woolhouse's method, Hardy's 
plan for computation. Garment, D. I. Act. 
J. 24 (1884) 224-. 

peerage mortality. Berridge, G. W. 
Assur. Mg. 12 (*1866) 220-. 

by summation. Todhunter, E. I. Act. J. 
32 (1896) 378-. 

, Woolhouse's method. Sprague, T. B. 

I. Act. J. 29 (1892) 59-, 232-. 
Grant of policies without further payments 

(after certain time). Sprague, T. B. Assur. 

Mg. 7 (*1858) 58-. 
Great powers (of Europe). Farr, W. Assur. 

Mg. 6 (*1857) 147-. 
Growth of children. Boas, F. Science 19 

(1892) 256-, 281-. 
, human, mathematical theory. Lehmann, 

J. W. H. D. Nf. Vsm. B. (1843) 299-. 
Height and weight of man, relation between. 

Macaulay, T. B. I. Act. J. 23 (*1882) 62-. 
Human will and chances, comparison. Guy, 

W. A. Assur. Mg. 5 (*1855) 315-. 

probability theory. Adan, H. I. 
Act. J. 33 (1898) 523-, 527-. 

. Young, T. E. I. Act. J. 33 

524-, 529-. 



Human will, uniform action. Lazarus, 

Assur. Mg. 3 (*1853) 169-. 
-- , -- . Hopf, G. Assur. Mg. 3 (*1853) 

Immediate annuities, series for expressing. 

Merrifield, C. W. Assur. Mg. 3 (*1853) 

324-. 
Importation of animal, vegetable and mineral 

substances into the Clyde, 1853-1857. 

Connal, M., & Keddie, . B. A. Ep. 28 

(1858) 185-. 
--- and vegetable substances (Liverpool, 

1851-55). Archer, T. C. B. A. Ep. (1857) 

Incomplete years of exposure, treatment. 

Lidstone, G. J. I. Act. J. 31 (1895) 304-. 
Increasing annuities and assurances, approxi- 

mate calculation. Lidstone, G. J. I. Act. 

J. 31 (1895) 68-. 

and decreasing premium scales. Laundy, 
S. L. Assur. Mg. 10 (*1863) 286-. 

reversionary charges. Paterson, W. B. 
I. Act. J. 35 (1901) 245-. 

Index, best means of constructing. Curtis, 
F. A. Assur. Mg. 8 (*1860) 54-. 

numbers, use in investigation of trade 
statistics. Bourne, S. B. A. Ep. (1885) 
859-. 

Industrial assurances, observations. Eea, C. 

H. E. I. Act. J. 34 (1899) 105-. 
Inordinate mortality, how far controllable by 

human agency. Porter, H. W. Assur. Mg. 

9 (*1861) 12-, 89-, 149-. 
Insanity in Scotland. Mitchell, (Sir) A. 

I. Act. J. 28 (1890) 426-, 432-. 
Insolvency in life assurance companies. Bailey, 

A. H. I. Act. J. 16 (*1872) 389-. 
Insolvent companies, liquidation and recon- 

struction. Sprague, T. B. I. Act. J. 16 

(*1872) 229-. 
Integral for compound survivorship annuity, 

approximate evaluation. Todhunter, R. I. 

Act. J. 33 (1898) 311-. 
Intellectual and moral statistics of France. 

Fayet, . C. E. 11 (1840) 565-. 
Interest, abridged multiplication applied to. 

Burnier, F. [1872] Laus. Bll. S. Vd. 11 

(1873) 362-. 

accounts. De Morgan, A. Assur. Mg. 10 
(*1863) 281-. 

-- . T.,A.H. Assur. Mg. 10 (*1863) 357-. 

and annuities, demonstration of formulae. 
De Morgan, . Assur. Mg. 4 (*1854) 277-. 

, calculation, method. Perkins, G. R. 
Silliman J. 47 (1844) 51-. 

, capitalising in course of year. Radell, . 
Grunert Arch. 2 (1842) 68-. 

, compound. Adams, Jas. Thomson A. 
Ph. 4 (1822) 450-. 

, . Lobatto, R. Quetelet Cor. Mth. 6 
(1830) 195-. 

, . Brassinne, E. N. A. Mth. 9 (1850) 
403-. 

, , and annuities : to find p from relation 



Z. Mth. Ps. 22 (1877) 190-. 



Ill 



1635 



Theory of Statistics. Actuarial Mathematics 



1635 



Interest, compound, average amount of sum at. 

Smith, H. A. I. Act. J. 14 (*1869) 158-. 
, , calculated by trigonometrical functions. 

Vervaet, P. Casopis 13 (1884) 264-; Fschr. 

Mth. (1884) 211. 
, , continuously reckoned. Studnicka, F. 

J. Casopis 2 (*1873) 85-; Fschr. Mth. 

(*1873) 609. 
, , and current accounts. Starkov, A. 

N. Es. S. Nt. Mm. (Mth.) 3 (*1881). 
, , curve. Carpenter, F. D. Y. V. Nost. 

Eng. Mg. 25 (1881) 385-. 
, , formulae. Scherling, C. Grunert 

Arch. 2 (1842) 213-. 
, , infinitesimal. Ferriot, . N. A. Mth. 

2 (1843) 461. 
, , . Dutoit, A. L. Laus. Bll. S. Vd. 

5 (1857) 169-. 
, , new formula for calculating. Catalan, 

E. C. As. Fr. C. E. 1 (1872) 141-. 
, , payable "momently." Young, (Dr) T. 

Ph. Mg. 2 (1827) 332-. 
_, _, powers, &c. Berdelle, C. As. Fr. C. 

E. 8 (1879) 170-. 
, , a result of. Bienaymg, J. Par. S. 

Phlm. PV. (1839) 60-. 
t and simple, equivalence. De Morgan, A. 

Assur. Mg. [1 (*1861)] 335-. 
, , solution of problems, without tables. 

Adler, M. N, I. Act. J. 23 (*1882) 359-. 
, , theory. Borgogelli, M. Em. N. Line. 

At. 47 (1894) 68-. 
, , time required to attain given amount. 

Studnicka, F. J. Casopis 13 (1884) 238-; 

Fschr. Mth. (1884) 210-. 
, equation of payment. Schlechter, . 

Grunert Arch. 34 (I860) 291-. 
, , extension of term, company's 

accounts. Schlechter, . Schlomilch Z. 

5 (1860) 214-. 
, fall in rate. Burn, J. I. Act. J. 34 (1899) 

474-. 
, laws of. Montel, E. de. C. E. 124 (1897) 

224-. 

payment, theory. Orlov, A. Kazan S. Nt. 
(Ps.-Mth.) P. 4 (1886) 250-. 

, question of. Orchard, W. Assur. Mg. 4 

(*1854) 61-. 
, . Gompertz, B. Assur. Mg. 4 (*1854) 

245-. 
, . I. Assur. Mg. 4 (*1854) 253-. 

rate, approximations in calculating reduc- 
tion. Stewart, J. I. Act. J. 32 (1896) 
261-. 

in certain investments, approximation. 

M. Assur. Mg. 6 (*1857) 54-. 
, short periods. Kelland, P. Edinb. E. S. 

P. 3 (1857) 274-. 
, simple or compound. Wittstein, T. 

Grunert Arch. 40 (1863) 240-. 
, . Oettinger, L. Grunert Arch. 

40 (1863) 243-. 

at 6 per cent., method of computing. 
Philomath. [Pseudon.] (vi Adds.) Bost. 
Mm. Am. Ac. 1 (1785) 174-. 

, theoretical and practical. Crelle, A. L. 
[1852] Crelle J. 49 (1855) 349-. 



Interpolation from irregular series. De Forest, 

E. L. Smiths. Ep. (1871) 275-; (1873) 

319-. 
Invalid lives, practice of certain assurance 

companies. Pinckard, G. H. Assur. Mg. 

[1 (*1861)] 273-. 
Invalidity probabilities, formulas. Samot, D. 

J. A. I. Act. J. 21 (*1879) 288-. 
Investments of funds of assurance companies. 

Brown, S. Assur. Mg. 7 (*1858) 241- . 
Isolated reversions. Shaw, C. G. Assur. Mg. 

2 (*1852) 295-. 

Issue of (hitherto) childless marriage, pro- 
bability. Sprague, T. B. I. Act. J. 22 

(*1881) 117-. 
Joint life annuity tables, method of finding 

D numbers. Henry, J. I. Act. J. 14 

(*1869) 212-. 

lives' assurance, table. Braid, W. Assur. 
Mg. 5 (*1855) 350, 363-. 

Land, price of, and purchase by the State, 
mathematical theory. Walras, L. [1880] 
Laus. S. Vd. Bll. 17 (1881) 189-. 

Landed property, theory of yield of soil applied 
to valuation. Pasini, V. Yen. At. 4 (1845) 
388-. 

Last r survivors of m lives, value of annuity. 
King, (?. I. Act. J. 22 (*1881) 293-. 

survivor of three lives, annuity found by 
actuaries' tables. Smyth, E. I. Act. J. 
17 (*1873) 379-. 

, value of annuity. Godicard, 

W. I. Act. J. 17 (*1873) 266-. 
Law of large numbers. Poisson, S. D. C. E. 

2 (1836) 377-. 

(Quetelet's) in intellectual mani- 
festations of man. Bitnicz, L. (xn) Mag. 

Ak. Ets. (1851) 241-. 
Leaseholds, renewals. Bunyon, C. J. Assur. 

Mg. 3 (*1853) 280-. 
Leases; perpetual renewal. Adams, Jas. 

Thomson A. Ph. 2 (1821) 307- ; 3 (1822) 

12-. 
, Sir Isaac Newton's table. De Morgan, A. 

Assur. Mg. 9 (*1861) 185-. 
, value. B., W. (vi Adds.) Thomson A. 

Ph. 10 (1825) 335-. 
" Leipzieger Krankencasse." Lazarus, W. 

Assur. Mg. 8 (*1860) 351-. 
Liabilities of assurance companies, estimate. 

Tucker, B. Assur. Mg. 10 (*1863) 312-. 
, . Bailey, A. H. Assur. Mg. 

11 (*1864) 111-. 

, , Bailey's. Sprague, T. B. 
Assur. Mg. 12 (*1866) 113-. 

. , valuation. Sprague, T. B. 
Assur. Mg. 11 (*1864) 90-. 

connected with buildings, estimation of 
value, with view to settlement by sum of 
money or annual payment. Eminich, W. 
Z. Bauw. 1 (1851) 195-. 

Liability of assurance company, estimation. 

Sprague, T. B. I. Act. J. 15 (*1870) 411-. 
Life assurance. Littrow, J. J. von. Baum- 

gartner Z. 9 (1831) 257-. 
. Sang, E. Edinb. T. Sc. S. Arts 1 

(1841) 339-, 349-, 360-, 394-. 



112 



1635 



Theory of Statistics. Actuarial Mathematics 



1635 



Life assurance. Rieu, A. [1872] Laus. Bll. 

S. Vd. 11 (1873) 269-. 
. Landre, C. L. N. Arch. Wisk. 12 

(1886) 182- ; Fschr. Mth. (1885) 194-. 

, applications suggested by 1851 census. 
Scott, G. Assur. Mg. 6 (*1857) 47-. 

, average risk. Kanner, M. I. Act. J. 

14 (*1869) 439-. 

calculations, modern methods of com- 
putation. Laundy, S. L. Assur. Mg. 8 
(*1860) 58-. 

, . "Milne, J." Assur. 

Mg. 8 (*1860) 118-. 

companies in Austria. Daninos, S. A. 
Assur. Mg. 3 (*1853) 121-. 

Germany. Hopf, G. Assur. Mg. 

3 (*1853) 134-, 220- ; 9 (*1861) 42-. 
, solvency. Macfadyen, J. R. [1870] 

Glasg. Ph. S. P. 7 (1871) 221-. 

compositions, notation for use in. 
Lazarus, W. Assur. Mg. 12 (*1866) 48-. 

contracts, reservations. Paraira, M. C. 

N. Arch. Wisk. 16 (1889) 215- ; Fschr. Mth. 

(1889) 229. 
, defects in system (1831). Fraser, W. 

Edinb. N. Ph. J. 11 (1831) 118-. 
, formulae connected with. Rubenson, R. 

Stockh. Ofv. (1891) 463-. 
in France. Curtis, F. A. I. Act. J. 

19 (*1876) 414-. 
fund, progress of profit. Searle, T. J. 

I. Act. J. 30 (1893) 493-. 
, Hillman's tables, errors in. Laundy, 

S. L. Assur. Mg. 9 (*1861) 239-. 
, mathematical theory. Samot, D. J. A. 

N. Arch. Wisk. 5 (*1879) 35-; 6 (*1880) 

124-. 

, , use of mortality statistics. 
Landre, C. L. N. Arch. Wisk. 10 (1884) 18-. 

, mean gain or loss for whole duration of 

assurance. Dienger, J. [1877] Epm. Mth. 
2 (1879) 89-. 

, premium, basis of determination. 
Weninger, V. (xn) [1861] Mag. Ak. Ets. 
(Mth. Term.) 2 (1861-62) 193-. 

, reserve. Gobbi, U. Mil. I. Lomb. 

Ed. 29 (1896) 612-. 
premiums, calculation. Stamkart, F. J. 

N. Arch. Wisk. 2 (*1876) 97-. 
, renunciation of payment. Rieu, A. 

Laus. Bll. S. Vd. 9 (1866-68) 361-. 

; present worth, and annual payment. 
Stamkart, F. J. Arch. Wisk. Gn. 2 (1860- 
63) 314-. 

, theory. Malmsten, C. J. Crelle J. 

Mth. 83 (1877) 245-; Acta Mth. 1 (1882) 
63-. 

assurances, mean error in. Gram, J. P. 
Ts. Mth. 6 (1889) 97-, 184- ; Fsch. Mth. 
(1888) 232-. 

contingencies, old and new methods for 
finding. Gray, P. Assur. Mg. [1 (*1851)] 
96 bis-. 

, problem. Gray, P. I. Act. J. 21 
(*1879) 67-. 

, valuation. Gompertz, B. Phil. Trans. 

(1820) 214-. 



Life contingencies, valuation. Hargreave, C. J. 
Ph. Mg. 5 (1853) 39-. 

contingency calculation, improvement. 
Farren, E. J. Assur. Mg. 5 (*1855) 185- ; 
8 ("I860) 121-. 

, solution of problems concerning. F., 

E. J. Assur. Mg. [1 (*1851)] 92 bis, 355-. 

expectation. Willich, C. M. Assur. Mg. 7 
(*1858) 181-. 

. Biden, W. D. Assur. Mg. 7 (*1858) 

352-. 
. Willich, C. A. M. Assur. Mg. 8 

(*1860) 139-. 
, meaning of phrase. Sprague, T. B. 

Assur. Mg. 13 (*1867) 381-. 

expectations. Landre, C. L, N. Arch. 
Wisk. 15 (1888) 22-; Fschr. Mth. (1888) 
237-. 

, formulae connected with. Geer, P. van. 

N. Arch. Wisk. 12 (1886) 60- ; Fschr. Mth. 
(1885) 194. 

experience in 1863, remarks. Tilt, R. R. 
I. Act. J. 32 (1896) 1-. 

interests and reversions, formula and tables. 
Nightingale, H. E. I. Act. J. 30 (1893) 9-. 

office, estimation of liability. Garment, D. 
I. Act. J. 21 (*1879) 74-. 

, tabulation of facts in records. Sprague, 

T. B. I. Act. J. 31 (1895) 205-. 

valuations, principles. McCandlish, 
J. M. I. Act. J. 20 (*1878) 12-. 

, probability and mean duration, Geneva 
1761-1813. Odier, L. Bb. Brit. 55 (1814) 
213-. 

risks, assessment. Chisholm, J. I. Act. J. 
25 (1886) 408-. 

tables, construction. Farr, W. Phil. Trans. 
(1859) 837-. 

, Gray's method of construction. 
Hannyngton, J. C. I. Act. J. 21 (*1879) 
455-; 22 (*1881) 136-. 

of Institute of Actuaries. Pell, M. B. 

I. Act. J. 21 (*1879) 137-. 
. Sprague, T. B. I. Act. J. 

21 (*1879) 452-. 
, Philadelphia. Chase, P. E. [1869] 

Am. Ph. S. P. 11 (1871) 17-. 

tenant and reversioner, apportionment 
between. Baden, A. I. Act. J. 16 (*1872) 
269-. 

, . Sprague, T. B. I. Act. J. 

18 (* 1875) 77-. 
Limitation of risks. Sprague, T. B. Assur. 

Mg. 13 (*1867) 20-. 
Limited and contingent interests in property. 

Bunyon, C. J. I. Act. J. 18 (*1875) 1-. 
Lives, and joint lives, values. Young, (Dr) T. 

Tilloch Ph. Mg. 47 (1816) 3-. 
Loading premiums. Makeham, W. M. I. Act. 

J. 15 (* 1870) 354-. 
. Smith, H. A. I. Act. J. 20 (*1878) 

145-. 
. Crisford, G. S. I. Act. J. 25 (1886) 

184-, 387-. 
Loans, arithmetical theory. Ronchetti, F. G. 

Mt. 24 (1886) 242-. 
, railway. Hultman, F. W. Ts. Mt. Fys. 3 

(1870) 278-. 



113 



1635 



Theory of Statistics. Actuarial Mathematics 



Morrison, R. Assur. Mg. 11 



Loans repayable by instalments. Makeham, 

W. M. I. Act. J. 18 (*1875) 132-. 
, interest rate. Gray, P. I. Act. J. 

14 (*1869) 91-, 182-, 397-. 
Longevity and expectation of life in United 

States. Worcester, J. E. [1825] Bost. Mm. 

Am. Ac. 1 (1833) 1-. 
, human. Ponzi, G. Tortolini A. 7 (1856) 

417-. 
, increase in France, 1770 to 1845. Dupin, 

G. C. E. 26 (1848) 585-, 613-. 

of inhabitants of Ipswich and Hingham. 
Wiggles-worth, E. [1782] Bost. Mm. Am. 
Ac. 1 (1785) 565-. 

Lubbock's formula of summation. Sprague, 
T. B. I. Act. J. 22 (*1881) 55-. 

Machinery, effect on public wealth, and wages 
fund. Tozer, J. Camb. Ph. S. T. 6 (1838) 
507- . 

Makeham's law. Quiquet, A. C. E. 106 

(1888) 1465-, 1569. 

, generalisation. Quiquet, A. C. B. 109 

(1889) 794-. 

Marine assurance. Flemmich, . Assur. Mg. 

2 (*1852) 102-. 

. Lance, W. Assur. Mg. 2 (*1852) 362-. 

at Hamburg. Lazarus, W. Assur. Mg. 5 

(* 1855) 221-. 
, principles. 

(* 1864) 285-. 

risks, statement of collisions. Rucker, J. A. 
Assur. Mg. [1 (* 1851)] 60-. 

Marriage, duration and number of surviving 
partners. Trembley, J. Berl. Mm. Ac. 
(1799-1800) 110-. 

, influence on death-rate in Scotland. Stark, 
J. [1866] Edinb. E. S. P. 6 (1869) 49-. 

and mortality tables combined. Chatham, 
J. I. Act. J. 28 (1890) 384-. 

Marriages, births, and deaths at St. Petersburg, 
tables. Krafft, W. L. [1798] St Pet. Ac. 
Sc. N. Acta 12 (1801) 246-. 

at different ages, proportion. Brown, S. 
Assur. Mg. 7 (*1858) 188-. 

Married woman's right of dower in real estate 
if she survives husband, table showing. 
Bowditch, J. I. Am. Ac. Mm. 1 (1833) 331-. 

Mean age, determination. Broca, P. Par. S. 
Ap. Bll. 2 (1879) 298-. 

duration of life. Ivernois, d\ Quetelet 
Cor. Mth. 8 (1834) 232-. 

rations of rural population of France. 
Hervt-Mangon, C. F. C. E. 79 (1874) 931-. 

Meaning of expression (1 - v). Gray, P. 

Assur. Mg. 10 (*1863) 117-. 
Median estimates. Galton, F. B. A. Ep. 

(1899) 638-. 
Medical statistics of life assurance companies. 

Porter, H. W. Assur. Mg. 4 (* 1854) 256-. 
Metals considered as money. Gergonne, J. D. 

Gergonne A. Mth. 21 (1830-31) 189-. 
Military assurance. Fischer, F. Hamb. Mth. 

Gs. Mt. 1 (1889) 4-. 
Monetary standard, variations in value. Brit. 

Ass. Comm. B. A. Ep. (1887) 247-; (1888) 

181- ; (1889)133-. 



1635 

Money and coin, theory. Murhard, F. W. A. 
Hermbstadt Ms. 1 (1814) 374-; 2 (1814) 1-. 

-lending. Weninger, V. (xn) Mag. Ak. 
Ets. (Mth. Term.) 4 (1863) 147-. 

, moral importance, two views. Czuber, (or 
Cuber) E. Arch. Mth. Ps. 62 (1878) 267-. 

Moral statistics. Quetelet, L. A. J. Brux. 
Ac. Sc. Mm. 21 (1848) 112 pp. 

values. Henderson, R. [1895] N. Y. Am. 
Mth. S. Bll. 2 .(1896) 46-. 

Mortality. 

ages 75 to 81. Thomson, W. T. Assur. Mg. 

[1 (*1851)] 29 Ms-. 
American assured lives. Brown, S. Assur. 

Mg. 8 (*1860) 184-. 
and annuity tables. Brown, S. I. Act. J. 16 

(* 1872) 428-. 
arising from military operations. Hodge, W.B. 

Assur. Mg. 7 (*1858) 80-, 151-, 201-, 275-. 
naval operations. Hodge, W. B. Assur. 

Mg. 6 (*1857) 254-. 
assured lives. King, G. I. Act. J. 19 (*1876) 

381- ; 20 (* 1878) 233-. 
in France. Hardy, G. F. I. Act. J. 33 

(1898) 485-. 
West Africa. L., A. I. Act. J. 33 

(1898) 516-. 
Indies. Hardy, G. F., d' Rothery, 

H. J. I. Act. J. 27 (1889) 161-. 
British Army and Navy. McLauchlan, J. J. 

I. Act. J. 34 (1899) 251-. 
canton of Geneva. Espine, M. d\ Bb. Un. 26 

(1840) 255- ; 55 (1845) 124-. 
children, Tasmania. Nowell, E. C. Tasm. E. 

S. P. (1875) 108-. 
the clergy. Stiissi, H. I. Act. J. 18 (*1875) 

343-. 
Danish clergy, 1650-1878. Westergaard, H. 

I. Act. J. 23 (*1882) 29-. 
depositors in Norwegian widows fund (1846- 

1872). Broch, O. J. N. Mg. Ntvd. 21 

(1876) 167-. 
determination from population statistics. 

Knapp, (Dr) [G. F.] II Polit. 4 (1867) 

(Tech.) 17-, 91-, 181-, 313-, 452-. 
from different diseases, influence of selection. 

Dovey, W. R. I. Act. J. 23 (*1882) 285-. 
English clergy, Hodgson's tables. Bowser, 

W. A. I. Act. J. 17 (*1873) 328-. 
, . Brown, S. I. Act. J. 17 (* 1873) 

339. 
equations and curves. Isely, L. Neuch. S. 

Sc. Bll. 17 (1889) 38-. 
estimation of, with migrant elements. Kiittner, 

W. Z. Mth. Ps. 38 (1893) 148-. 
experience of Scottish Amicable Assurance 

Society. Spens, W. Assur. Mg. 10 (*1863) 

61-, 197-. 
Finland. Lindelof, L. Helsingf. Bd. 49 

(1890) 115-. 

and some other countries. Lindelof, L. L. 
Helsingf. Ofv. 15 (1873) 129-. 

France between 20 and 25, and 25 and 30, 
compared with other countries. Espine, 
M. d'. Bb. Un. Arch. 5 (1859) 220-. 



114 



1635 Mortality 

Glasgow and other cities. Macfadyen, J. R, 

Glasg. Ph. S. P. 7 (1871) 425-. 
government officials on West Coast of Africa. 

Hart, J. R. I. Act. J. 33 (1898) 307-. 
hourly distribution. Lawson, R. I. Act. J. 

19 (*1876) 110-. 
of infants in Scotland. Robertson, W. I. Act. 

J. 22 (* 1881) 140-. 
influence of high and low prices on rate. 

Barton, J. (n Adds.) Ph. Mg. 5 (1834) 

278-. 
innkeepers, publicans, etc. Stott, J. I. Act. 

J. 20 (*1878) 35-. 
law. Edmonds, T. R. Assur. Mg. 9 (*1861) 

170- . 

. Lazarus, W. Assur. Mg. 10 (* 1863) 283-. 
. Makeham. W. M. Assur. Mg. 13 (*1867) 

325-. 
, answer to De Morgan's criticism. Gompertz, 

B. Assur. Mg. 9 (* 1861) 296-. 

, British India. Henderson, H. B. As. 
Kesearches 20 (1836) 190-. 

and construction of annuity tables. 
Makeham, W. M. Assur. Mg. 8 (*1860) 
301-. 

, empirical expression. Buniakovskij, V. Ja. 

St Pet. Ac. Sc. Mm. (Rs.) 15 (*1869) 

(Suppl.) No. 4, 20 pp. 
, expectation of life and values of annuities 

in India and England. Hannyngton, J. C. 

Beng. J. As. S. 12 (1842) 1057-. 
, expression by geometrical series. Wool- 
house, W. S. B. Assur. Mg. 11 (* 1864) 150-. 
, Makeham's modification of Gompertz's 

theory. Gray, P. Assur. Mg. 11 (*1864) 

236-. 
, mathematical. Young, T. E. I. Act. J. 

22 (*1881) 139-. 

_ , _. Wittstein, T. I. Act. J. 24 (1884) 
' 153- ; 33 (1898) 399-. 
, mode of determining life contingencies. 

Gompertz, B. Phil. Trans. (1825) 513-. 

from observations. Hattendorff, K. Gott. 
Nr. (1871) 382-. 

laws. Jellicoe, C. B. S. P. 4 (1839) 115. 

of Gompertz and Makeham. Bertrand, J. 

C. B. 106 (1888) 1042-. 

Manchester and Salford. Henry, T. [1786] 
Manch. Ph. S. Mm. 3 (1790) 159-. 

and marriage of Europeans in India. Brown, 
S. [1862] Assur. Mg. 11 (* 1864) 1-. 

experiences, certain. Hewat, A., & 
Chatham, J. I. Act. J. 31 (1895) 428-. 

Massachusetts. Elliott, E. B. Am. As. P. 

(1857) 51-. 
miners in district of Marazion. Couch, R. Q. 

Cornwall Pol. S. T. (1860) 18-. 
St Ives and of agricultural popula- 
tion of St Buryan. Couch, R. Q. Cornwall 

Pol. S. T. (1859) 30-. 
St Just. Couch, R. Q. Cornwall 

Pol. S. T. (1857) 1- ; (1858) 1-. 
officers in the army, 1824-1873. Alvord, B. 

Am. As. P. 23 (1874) (pt. i.) 57-. 
Paris and London. Tite, W. B. A. Bp. 34 

(1864) (Sect.) 177-. 
periodical observation, scheme for. Curtis, 

F. A. I. Act. J. 19 (*1876) 229-. 



Mortality 1635 

from peritonitis (males and females) between 

fifteen and fifty. Robertson, W. I. Act. J. 

19 (* 1876) 118-. 
Philadelphia, 1809-1816. Vaughan,J. [1817] 

Am. Ph. S. T. 1 (1818) 430-. 
and population laws in France. Demon/errand, 

F. Par. EC. Pol. J. 16 (26 e cah.) (1838) 249-. 
probabilities. Landre, C. L. N. Arch. Wisk. 

10 (1884) 26-. 
progressive. Meikle, J. Assur. Mg. 3 (* 1853) 

province of Bologna. Predieri, P. N. A. Sc. 

Nt. 7 (1847?) 396- ; 8 (1847) 31-. 
rate on assured lives, effect of withdrawals. 

Gray, W. T. I. Act. J. 24 (1884) 256-. 
, . Sprague, T. B. I. 

Act. J. 24 (1884) 293-. 
in West Indies. Stott, J. I. Act. 

J. 21 (*1879) 153-. 

in certain parts of Africa. Sprague, A. E. 
I. Act. J. 33 (1898) 285-. 

, De Wit's theory. Orchard, W. Assur. 
Mg. 2 (*1852) 393-. 

deduced from experience of assured lives. 
Whittall, W. J. H. I. Act. J. 31 (1895) 
161-. 

in early manhood. Bailey, A.H. I. Act. J. 
14 (* 1869) 247. 

among emigrants. McLauchlan, J. J. I. 
Act. J. 18 (*1875) 381-. 

Europeans in India. Sprague, T. B. 
I. Act. J. 19 (*1876) 295-. 

Jamaica. Marshall, J. Assur. 

Mg. 4 (*1854) 39-. 
, experience of an assurance company. 

Jellicoe, C. Assur. Mag. 4 (*1854) 199-. 

and its increase. Chatham, J. I. Act. J. 
29 (1892) 81-. 

in India. Finlaison, A. J. I. Act. J. 18 
(*1875) 153-. 

infancy and childhood. Bowser, W. A. 

I. Act. J. 17 (* 1873) 26-. 

as influenced by time of assurance. Sprague, 
T. B. I. Act. J. 15 (* 1870) 328-. 

among Jews. Sprague, T. B. I. Act. J. 27 
(1889) 155- . 

in navy. Sprague, T. B. I. Act. J. 25 
(1886) 49-. 

New South Wales. Pell, M. B. N. S. 

W. B. S. T. 1 (1867) 66-; I. Act. J. 21 
(*1879) 257-. 

peerage during nineteenth century. 
Bailey, A. H., & Day, A. Assur. Mg. 9 
(*1861) 305-. 

select lives. Spens, W. Assur. Mg. 12 

(*1866) 304. 

throughout life, formula. Thiele, T. N. 
I. Act. J. 16 (*1872) 313-, 464. 

, Zeuner's method for determining. 

Danielewicz, B. Prace Mt.-Fiz. 6 (1895) 

183-. 
rates in Australia. Burridge,A. F. I. Act. J. 

24 (1884) 333-. 

as disturbed by migrations. Welton, T. A. 
I. Act. J. 16 (* 1872) 153-. 

, methods for deducing. Ackland, T. G. I. 
Act. J. 33 (1898) 68-, 131-. 

115 H 2 



1635 Mortality 

rates, methods for deducing discontinuances. 
Todhunter, R. I. Act. J. 33 (1898) 273-. 

of natives and Europeans in India. Brown, 
S. I. Act. J. 16 (* 1872) 187-. 

of India. Hardy, G. F. I. Act. J. 25 

(1886) 217-. 

and their causes. Lazarus, W. I. Act. J. 
18 (* 1875) 54-, 212-. 

in United States. Gill, . Assur. Mg. 3 
(*1853)300-. 

Victoria. Burridge, A. F, I. Act. J. 23 

(*1882) 309-. 
ratio in Europe. Dieterici, G. F. W. Berl. 

Ab. (1851) (Ph.) 721-. 
in relation to age and sex. Bertillon, (Dr) . 

Fr. Cg. Md. Chir. 3 (1866) 663-. 
Salem, 1782 and 1783. Holyoke, E. A. Bost. 

Mm. Am. Ac. 1 (1785) 546-. 
among Sardinian soldiers in times of peace. 

Bonino, J. J. Tor. Mm. Ac. 35 (1831) 

233-. 
selected classes. Demonferrand, F. C. R. 9 

(1839) 244-. 
lives in Germany. Brune, . Assur. Mg. 

3 (* 1853) 29-. 
, inadequacy of data. Spens, W. Assur. 

Mg. 4 (* 1854) 1-, 139-. 
shifting population. Wittstein, T. Grunert' 

Arch. 39 (1862) 67-. 
and sickness among labouringclasses. Edmonds, 

T. R. Assur. Mg. 5 (*1855) 127-. 
statistics, collection. Sang, E. I. Act. J. 15 

(* 1870) 257-. 
, formula. Westergaard, H. (xn) Ts. Mth. 

1 (1877) 1-. 
, . Enestrom, G. Stockh. Ofv. (1891) 

185- ; Fschr. Mth. (1891) 241-. 
supplement to two papers in Phil. Trans. 1820, 

1825. Gompertz, B. [1861] Phil. Trans. 

(1862) 511-. 
and survival at different ages in Geneva, 1838- 

1845. Espine, M. d'. Gen. Mm. S. Ps. 11 

(1846) 457-. 
table for Brabant. Quetelet, L. A. J. Brux. 

Ac. fill. 6 (1859) 345-. 

deduced from new experience. Bowser, 
W. A. I. Act. J. 16 (*1872) 146-. 

whole life premium table. Wylie, W. 

Assur. Mg. 2 (*1852) 391-. 
, Northampton, mode of construction. 

Sutton, W. I. Act. J. 18 (*1875) 107-. 
tables. Weninger, V. (xn) [1860] Mag. Ak. 

Ets. (Mth. Term.) 2 (1861-62) 51-. 

in America. McCay, C. F. I. Act. J. 16 
(* 1872) 20-. 

, arrangement of data. Meikle, J. Assur. 

Mg. 13 (*1867) 261-. 
, Bengal Civil Service. Hannyngton, J. C. 

Beng. J. As. S. 19 (1850) 250-. 
, calculation. Quetelet, L. A. J. Brux. Ac. 

Bll. 19 (1852) (pte. 3) 289-. 
, comparison. Young, (Dr) T. QJ. Sc. 2 

(1828) 342-. 
, computation. Thiele, T. N. Kj0b Ov 

(1900) 139-. 
, construction. Woolhouse, W. S. B. Assur. 

Mg. 13 (* 1867) 75-. 



Theory of Statistics, etc. 1635 

Mortality, continued. 

tables, construction. Baumhauer, M. M. von. 

I. Act. J. 16 (* 1872) 34-. 
, from imperfect data. Makeham, W. M. 

I. Act. J. 16 (* 1872) 344-. 
, , principles of. Makeham, W. M. Assur. 

Mg. 12 (* 1866) 305- . 

for Finland. Lindelof, L. Helsingf. Ofv. 
38 (1896) 113- . 

, formulae. Enestrom, G. Stockh. Ofv. 

(1891) 251-, 343-; Fschr. Mth. (1891) 242-, 

243-. 
, for calculating. Enestrom, G. Stockh. 

Ofv. (1891) 441- ; Fschr. Mth. (1891) 244-. 

and policy values. Meikle, J. I. Act. J. 23 
(*1882) 385-. 

, select, construction and use. Sprague, 

T. B. I. Act. J. 21 (* 1879) 229- ; 22 (* 1881) 

391-. 
, theory- Samot, D. J. A. N. Arch. Wisk. 

3 (*1877) 145-. 
United States of America. Brown, S. Assur. 

Mg. 13 ( 1867) 272-. 
various .classes. Hardy, G. F. I. Act. J. 23 

(* 1882)1-. 

countries of Europe. Anon, (vi 354) 
Edinb. N. Ph. J. 16 (1834) 259-. 



Movement of population, diocese of Maurienne, 

1810-1830. Anon, (vi 1123) Sav. Mm. 

Ac. 5 (1831) 255-. 
, France. Demon/errand, F. C. E. 2 

(1836) 437-. 
, Macon and environs, 1740-1828. 

Benon des Chanes, . (xn) Macon S. C. E. 

(1828) 65-. 
, Palermo. Villot, . A. Sc. Nt. 10 

(1827) 442-. 
, Paris. Villerme, L. A. Sc. Nt. 8 

(1826) 423-. 
-, Portugal. Silva, D. A. da. Lisb. J. 

Sc. Mth. 2 (1870) 255-. 
, Spain, 1866. La Sagra, R. de. 

C. B. 67 (1868) 460-. 
Multiple annuities, formation of values and 

amounts. Gray, P. I. Act. J. 24 (1884) 

129-. 
Mutual life assurance, theory. Templeton, 

J. M. I. Act. J. 20 (*1878) 77-. 
Negative policy values. Deuchar, J. J. W. 

I. Act. J. 19 (*1876) 97-. 
. Gray, W. T. I. Act. J. 20 (*1878) 

73-, 150-. 
. King, G. I. Act. J. 20 (*1878) 

148-. 
Net premium and interest rate. Sutton., W. 

I. Act. J. 17 (*1873) 446-. 

mode of valuation, objections to. 
Makeham, W. M. I. Act. J. 15 (*1870) 449-. 

present value of instruments of credit, etc. 
Ronchetti, F. G. Mt. 26 (1888) 133-. 

profits, possible methods of dividing. 
Wilbraham, H. Assur. Mg. 6 (*1857) 
278-. 

Number of white persons in United States, 
tables. Bowditch, J. I. Am. Ac. Mm. 1 
(1333) 345-. 



116 



1635 Theory of Statistics, etc. 

Obligations, contracting and discharge, theory. 

Boudsot, A. A. (xn) Doubs S. Mm. 2 

(1858) 340-. 
Obligatory assurance, theory. Enestrom, G. 

Stockh. Ofv. (1895) 807- ; Fschr. Mth. (1895) 

251-. 
Occupation, influence on health. Nelson, 

F. G. P. I. Act. J. 17 (*1873) 95-. 
Old age and invalid assurance, theory. 

Lazarus, W. Hamb. Mth. Gs. Mt. 2 (1890) 

(Festschr. Tl. 2) 158-. 
Orchard's tables and a theoretical mortality 

table. Gray, P. Assur. Mg. 6 (*1857) 

181-. 
"Paid up" policy as equivalent to policy 

payable. Macfadyen, J. E. I. Act. J. 15 

(*1870) 297-. 
Partial commutation of premium. Gray, P. 

I. Act. J. 17 (*1873) 224-. 

Payment of yearly premium. Wiegand, A. 

Assur. Mg. 12 (* 1866) 54-. 
. Laundy, S. L. Assur. Mg. 12 

(* 1866) 55-. 
Pension calculation, formula. Enestrom, G. 

Stockh. Ofv. (1893) 405- ; Fschr. Mth. 

(1893-94) 360-. 
Pensions. Lindelof, L. Helsingf. Ofv. 26 

(1884) 67-; Fschr. Mth. (1884) 189; 

Helsingf. Acta 14 (1885) 1-; 15 (1888) 209- ; 

Helsingf. Bd. 51 (1892) 43-; 54 (1894) 1-; 

Acta Mth. 18 (1894) 89-. 
. Widows and orphans fund of Leipzig 

University, 1882. Drobisch, M. W. Leip. 

Mth. Ps. B. 34 (1882) 51-. 
Perpetuity contingent on surviving four lives. 

M., T. Assur. Mg. 12 (*1866) 301. 
Philosophy of statistics. Woolhouse, W. S. B. 

I. Act. J. 17 (*1873) 37-. 
Policies of assurance and life interests. 

Sprague, T. B. Assur. Mg. 8 (*1860) 

, valuation. Anon. Assur. Mg. 10 

(*1863) 252-, 322-. 

on recently assured lives, reserve on. 
Teece, E. I. Act. J. 22 (*1881) 250-. 

, . Sprague, T. B. I. Act. 

J. 22 (*1881) 264-. 
Policy on longer of two lives, value. Carr, T. 

I. Act. J. 14 (*1869) 415-. 

valuation, subject to half yearly or quarterly 
premiums. Sprague, T. B., & King, G. I. 
Act. J. 23 (* 1882) 256-, 264-. 

value. Meikle, J. Assur. Mg. 11 (*1864) 
241-. 

and rate of interest. Sutton, W. I. Act. 

J. 17 (*1873) 227-. 
. Walton, W. G. I. Act. J. 

22 (*1881) 135-. 
tables, modes of constructing. Manly, 

H. W. I. Act. J. 15 (* 1870) 169-. 
in terms of premium. Wilding, R. I. 

Act. J. 22 (* 1881) 131. 

values, constructing models of. Chisholm, J. 
I. Act. J. 25 (1886) 141-. 

, effect of increased mortality. Sprague, 

T. B. I. Act. J. 21 (* 1879) 77-. 



Population 1635 

Policy values found by various methods, com- 
pared. Manly, H. W. I. Act. J. 14 (* 1869) 
249-. 

Political arithmetic. Czornig, K. J. Prag Jb. 
Bohm. Ms. 2 (1831) 22-. 
Whewell, W. \ 



economy. 



[1850] Camb. Ph. 



S. T. 9 (1856) 128- ; (pt. 2) [1]-. 

and arithmetic, laws. Balbo, P. Tor. 

Mm. Ac. 34 (1830) 47-. 

assurance, mathematical theory. 
Wittstein, T. I. Act. J. 17 (*1873) 178-, 
355-, 417-. 

, mathematics applied to. Eau, . 
Brux. Ac. S. Bll. 8 (1841) (pte. 2) 148-. 

, . Helm, G. Dresden Isis Sb. 

(1887) (Ab.) 3-. 
, . Edgeworth, F. Y. B. A. Rp. 

(1889) 671-. 

Population. 

Benares. Prinsep, J. As. Researches 17 

(1832) 470-. 
births, etc., in the Netherlands. Quetelet, 

L. A. J. Brux. Ac. Sc. Mm. 4 (1827) 117-. 
Bombay. Macintosh, J. Thomson A. Ph. 14 

(1819) 429-. 
British Isles. Coquebert de Montbret, (Baron). 

Par. S. Gg. Bll. 1 (1822) 191-. 
density, proposed units of areas. Steinhauser, 

A. Wien Mt. Gg. Gs. 7 (1863) 129-. 
France. Dupin, C. C. R. 28 (1849) 369-. 

in 18th and 19th centuries. Dupin, C. 
C. R. 1 (1835) 103-. 

, influence of price of corn. Dupin, C. 

C. R. 2 (1836) 585-. 
general considerations. Anon, (vi 703) J. de 

Ps. 93 (1821) 320-, 414-. 
general laws. Quetelet, L. A. J. Brux. Ac. 

Bll. 9 (1842) (pte. 2) 550-. 

. Pouillet, C. S. M. C. R. 15 (1842) 861-. 

(Pouillet). Demonf errand, F. C. R. 15 

(1842) 1096-. 
Geneva. Mallet, E. Gen. Mm. S. Ps. 7 

(1836) 321-. 
increase, 1770-1848. Carnot, H. C. R. 31 

(1850) 288-. 
, apprehensions caused by. Hoffmann, J. G. 

Berl. Ab. (1835) (Ph.) 121-. 

and decrease in Danish states. Callisen, . 
Dn. Vd. Selsk. Skr. 6 (1809-12) (2'. hceft.) 
169-. 

dependent on abundance of cereals and 
other foods. Predieri, P. N. A. Sc. Nt. 1 
(1850) 58-. 

in Europe and America, decrease of rate. 
Storer, H. E. [1858] Am. J. Sc. 43 (1867) 
141-. 

kingdom of Naples, decrease of rate. 
Augustinis, M. de. Ranuzzi An. Gg. (1845) 
35-. 

Prussia in town and country. Dieterici, 

C. F. W. Berl. Ab. (1857) (Ph.) 99-. 

relation to means of subsistence. 
Bourne, S. B. A. Rp. (1877) (Sect.) 165-. 

law of increase. Verhulst, P. F. Quetelet 
Cor. Mth. 10 (1838) 113- ; Brux. Ac. Sc. 
Mm. 18 (1845) 38 pp. ; 20 (1847) 32 pp. 



117 



1635 Population 

law of increase and decrease. Besnard, G. 

Caen Mm. Ac. (1856) 203-. 
duration of families. Bienayme, J. 

Par. S. Phlm. PV. (1845) 37-. 
during last 100 years. Edmonds, T. E. 

Assur. Mg. 2 (*1852) 57-. 
mathematical theory. Quetelet, L. A. J. 

L'l. 2 (1834) 311-. 
Mexico, 1840. Galeotti, H. G. Brux. Ac. Bll. 

8 (1841) (pte. 2) 95-. 

and mortality statistics, emigration and immi- 
gration being taken into account. Enestrom, 

G. Stockh. Ofv. (1896) 225- ; Fschr. Mth. 

(1896) 187-. 
movement, European birth- and death-rate. 

Benoiston de Chateauneuf, . A. Sc. Nt. 7 

(1826) 314-. 
Oceania, Penes Is. Cagnazzi, L. de S. Nap. 

Ed. 2 (1843) 118-. 
statistics, Austria, etc. Ficker, A. [1859] 

Wien Mt. Gg. Gs. 4 (1860) (Ab.) 71-. 
, generalisation from. Enestrom, G. Stockh. 

Ofv. (1896) 403- ; Fschr. Mth. (1896) 188. 
, theory of pensions. Enestrom, G. Stockh. 

Ofv. (1893) 361- ; Fschr. Mth. (1893-94) 

358-. 
theory. Vinde, . Eure J. d'Ag. 6 (1829) 

331-. 
white and slaves, increase in United States. 

Harvey, G. Edinb. Ph. J. 8 (1823) 41-, 

328-; 9 (1823) 63-. 
world, ancient and modern. Merritt, . Par. 

S. Gg. Bll. 9 (1828) 1-. 
, races, religions, etc. Dieterici, C. F. W. 

Peterm. Mt. (1859) 1-. 



Piemature death among select lives. Barren, 
E.J. Assur. Mg. 4 (* 1854) 66-, 141. 

Premium-obligation, worth for any period. 
Hultman, F. W. Ts. Mt. Fys. 4 (1871) 
251-. 

payable for life or for term, difference 
between. Meikle, J. Assur. Mg. 5 (* 1855) 
154-. 

rates and benefits accruing, incongruities. 
S., H. A. Assur. Mg. 8 (*1860) 167-. 

for Bengal. Jellicoe, C. Assur. Mg. 
[1 (*1851)] 166-. 

to provide certain periodical returns. 
Tucker, E. Assur. Mg. 9 (*1861) 245-. 

scales, use of reduced. Hardy, G. F. I. 
Act. J. 31 (1895) 261-. 

values, method of interpolating. Samot, 
D. J. A. I. Act. J. 20 (*1878) 347-. 

, . Garment, D. I. Act. J. 21 

(*1879) 213-. 
Premiums, calculation by Gompertz's law. 

Makeham, W. M. Assur. Mg. 9 (* 1861) 

361. 
, half yearly and quarterly, obtained from 

annual. Laundy, S. L. Assur. Mg. 11 

(*1864) 232-. 
Present value of payments (when reproductive 

differs from remunerative rate). Lidstone, 

G. J. I. Act. J. 33 (1898) 412-. 



Theory of Statistics, etc. 1635 

Present values, calculation. Heegmann, A. 

Lille Mm. S. (1827-28) 1-. 
Price of annuity for n years of life of a person 

aged x. Macfadyen, J. E. I. Act. J. 19 

(*1876) 141-. 
Probabilities, application to judicial statistics. 

Couniot, A. A. Liouv. J. Mth. 3 (1838) 257-. 
, therapeutic statistics and statistics 

generally. Hagenbach-Bischoff ', E. [1877] 

Basel Vh. 6 (1878) 516-. 

involved in widows' fund. Gruson, J. P. 
Berl. Ab. (1812-13) (Mth.) 1-. 

. Values of contingent reversions, 3 lives 
involved in survivorship. Morgan, W. [1799] 
Phil. Trans. (1800) 22-. 

Probability of duration, decrement and ex- 
pectation of life in New Hampshire and 
Massachusetts. Wigglesworth, E. Bost. 
Mm. Am. Ac. 2 (1793) 131-. 

election results. Korteiceg, D. J. [1875] 

Arch. Neerl. 12 (1877) 65-. 

, local. Enestrom, G. Stockh. Ofv. (1893) 
623-; Fschr. Mth. (1893-94) 363. 

of success of candidates for three- or four- 
cornered constituencies. Hayward, E. B. 

B. A. Rp. 38 (1868) (Sect.) 9-. 

Profit, determination and distribution. Meikle, 
J. Assur. Mg. 11 (* 1864) 251-. 

distribution in mutual assurance societies. 
Pell, . I. Act. J. 14 (*1869) 382-. 

Profits, formulas and tables for applying. 

Manly, H. W. I. Act. J. 27 (1889) 362-; 

28 (1890) 333-. 
, , note on Manly's paper. 

Calderon, H. P. I. Act. J. 28 (1890) 394-. 
Progressive taxation, theory. Gobbi, U. Mil. 

I. Lomb. Ed. 30 (1897) 452-. 
Property, division between children according 

to civil code. Catalan, E. C. L'l. 30 (1862) 

139-. 

held for life and in reversion, valuation. 
Jellicoe, C. Assur. Mg. 6 (*1857) 61-. 

, . Wilbraham, H. 

Assur. Mg. 6 (*1857) 211-. 

and income tax, inequitable distribution. 
Jellicoe, C. Assur. Mg. 2 (*1852) 213-. 

Proportional parliamentary representation. 
Wasteels, J. Mathesis 20 (1900) 81-. 

representation at elections. Curie, J. As. 
Fr. C. E. (1889) (Ft. 2) 993-. 

, methods. Enestrom, G. Stockh. Ofv. 

(1896) 543-; Fschr. Mth. (1896) 189. 

of minorities. Bayssellance, A. Bordeaux 

S. Sc. Mm. 3 (1880) 285-. 

Prosperity in nations, relation to ethical con- 
ditions and mental development. Dieterici, 

C. F. W. Berl. Ab. (1855) (Ph.) 433-. 
Purchasing life assurances as an investment. 

Day, A. Assur. Mg. 8 (*1860) 326-. 
Pure premium method of valuation. Bailey, 
A. H. I. Act. J. 21 (*1879) 115-. 

as affected by expense and 
selection. Sorley, J. I. Act. J. 21 (*1879) 
192-. 

Quinquennial census, deduction of yearly 
alterations. Enestrom, G. Stockh. Ofv. 
(1893) 541- ; Fschr. Mth. (1893-94) 362. 



118 



1635 



Theory of Statistics. Actuarial Mathematics 



1635 



Kailway production and renewal, mathematical 
theory of cost. Mohr, . Giving. 37 (1891) 
39-. 

travelling, economics. Schneidewind, A. 
Arg. S. Ci. A. 39 (1895) 5-; 40 (1895) 77-; 
41 (1896) 185-, 209-. 

, . Soulages, E. Arg. S. Ci. A. 42 

(1896) 337-. 

Eatio of newly contracted marriages to con- 
temporary population. Dieterici, C. F. W, 

Berl. Ab. (1856) (Ph.) 559-. 
Rationale of some actuarial estimates. Jellicoe, 

C. Assur. Mg. 8 (*1860) 310-. 
Eejection of fractions of 1 in extensive 

valuations. De Morgan, A. Assur. Mg. 10 

(*1863) 247-. 
Belation of births to deaths, effects of migration 

and affluence. Benon des Chdnes, . (xn) 

Macon S. C. E. (1824) 89-. 
Eelationship, human, algebra of. Macfarlane, 

A. [1879-81] Edinb. E. S. P. 10 (1880) 
224-; 11 (1882) 5-, 162- ; Ph. Mg. 11 1881 
436-. 

', , . Brunei, . Bordeaux S. Sc. 

Mm. 4 (1894) xxv-. 
, a problem in. Macfarlane, A. Edinb. E. 

S. P. 15 (1889) 116- . 
Eelationships (kinship), Gal ton's arithmetical 

notation. Macfarlane, A. Nt. 28 (1883) 588. 
Eeliability of data, as tested by conclusions. 

Farren, E. J. Assur. Mg. 3 (* 1853) 204-. 
Eemarriage rate of widowers. Sprague, T. B. 

I. Act. J. 22 (*1881) 77-. 
Eents and value of ground in Borne. Armellini, 

T. Em. N. Line. At. 27 (1874) 111-. 
Eeproduction table, English. Farr, W. Phil. 

Trans. 171 (1880) 281 -. 
Eeserves of assurances, Keuchel's formula. 

Danielewicz, B. Wiad. Mt. 2 (1898) 150-. 
with return of premium. Danielewicz, 

B. Wiad. Mt. 3 (1899) 275-. 

fixed term assurances, calculation. 
Danielewicz, B. Wiad. Mt. 2 (1898) 216-. 

on life assurances. Danielewicz, B. Wiad. 
Mt. 4 (1900) 60-. 

owing to different data of valuation. 
Valentine, J. I. Act. J. 18 (*1875) 229-. 

Eetirants in eighth year. Macaulay, T. B. 

I. Act. J. 22 (*1881) 134-. 
Eeturnable premiums, calculation. Makeliam, 

W. M. Assur. Mg. 12 (*1866) 233-. 
Eeversionary annuities. King, G. I. Act. J. 

22 (*1881) 296-. 
payable half yearly or quarterly. Carr, T. 

Assur. Mg. 7 (*1858) 109-. 
, etc. Sprague, T. B. I. 

Act. J. 15 (*1870) 126-; 18 (*1875) 76. 
, value of second nomination. Hardy, 

G. F. I. Act. J. 25 (1886) 134-. 

annuity, formula for. M., A. (Editor). 
Assur. Mg. 5 (*1855) 52. 

, . Sprague, T. B. Assur. Mg. 7 

(*1858) 174-. 
payable oftener than once a year, value. 

Evans, W. I. Act. J. 19 (*1876) 12-. 

bonus attaching to each policy, method of 
calculation. Hardy, E. P. I. Act. J. 31 
(1895) 330- . 



Eeversionary interests, certain contingent. 
Warner, S. G. I. Act. J. 31 (1895) 280-. 

life interests as securities for loans. 
Sprague, T. B. I. Act. J. 17 (*1873) 229-. 

, valuation. Sprague, T. B. I. Act. 

J. 14 (*1869) 417-. 
, . Davies, G. I. Act. J. 15 (* 1870) 

138-. 
, . Sprague, T. B. I. Act. J. 27 

(1889) 107-. 
, . Sunderland, A.W. I. Act. J. 27 

(1389) 220-. 

transactions by lifei. assurance companies. 
Macfadyen, J. E. I. Act. J. 20 (*1878) 
385-. 

Eisk premiums for survivorship assurances. 

Sunderland, A. W. I. Act. J. 27 (1889) 81-. 
Eisks of assurance, mode of tabulation. 

Chatham, J. I. Act. J. 32 (1896) 393-. 

in granting life assurance. Bremiker, C. 
I. Act. J. 16 (*1872) 216-, 285-. 

, valuation, and division of surplus. Jellicoe, 

C. Assur. Mg. 10 (* 1863) 328-. 
Eoyal Society, effect of limitation of number 

of fellows elected each year on eventual 

total. Strachey, (Lt.-Gen.) E. E. S. P. 51 

(1892) 463-. 
Savings banks. Dupin, C. C. E. 4 (1337) 

597. 
. Crelle, A. L. Crelle J. 39 (1850) 133-. 

, progressive development. Dupin, C. 
C. E. 17 (1843) 1008-. 

, statistics. Dupin, C. C. E. 20 (1845) 

1593-. 
Second marriages in the peerage. Day, A. 

Assur. Mg. 12 (*1866) 185-. 
Selection among assured lives. Higham, J. A. 

I. Act. J. 20 (* 1878)1-. 

of lives for assurance'. Thomson, S. C. 
I. Act. J. 21 (*1879) 170-. 

Sickness and invalidism, in relation to mor- 
tality. Makeham, W. M. I. Act. J. 16 
(*1872) 408-. 

mortality among native and European 

troops in India. Scales, W. H. Assur. Mg. 
5 (* 1855) 245-. 

, present state of information. Tomp- 

kins, H. Assur. Mg. 3 (* 1853) 7-. 

rate in France. Brown, S. Assur. 
Mg. 5 (*1855) 208-. 

tables, Eatcliffe's. Frankland, F. W. I. 
Act. J. 21 (*1879) 380. 

Simpson's rule, generalisation for joint life 

annuities. Allen, J. M. I. Act. J. 33 (1898) 

535-. 
Single and annual premium, proof of formulae. 

Gray, P. Assur. Mg. 10 (*1863) 238-. 
, . Wiegard,D.A. Assur. 

Mg. 10 (*1863) 286. 

life contingencies, calculation. De Morgan, 
A. Assur. Mg. 12 (*1866) 328-; 13 (*1867) 
129-. 

Sinking fund assurance. Faulks, J. E. I. 

Act. J. 34 (1899) 562-. 
Smoothing of mortality observations, and 

Oppermann's formula. Gram, J. P. Ts. 

Mth. 2 (1884) 113- ; Fschr. Mth. (1884) 

187-. 



119 



Theory of Statistics. Actuarial Mathematics 



1635 



Social statistics and uniform action of human 
will. Broicn, S. Assur. Mg. 2 (*1852) 
341-. 

Stability of results with reference to number of 
transactions. Campbell, R. Assur. Mg. 9 
(*1861) 216-. 

Standard weight of Cologne mark. Eytelwein, 
J. A. Berl. Ab. (1816-17) 42-. 

Statistical investigation of evolution. Cun- 
ningham, J. T. Nt. 51 (1894-95) 510. 

method for determining the vitality of a 
population, that of Sweden in particular. 
Enestrmn, G. Stoefch. Ofv. (1893) 481- ; 
Fschr. Mth. (1893-94) 361. 

rejection of extreme variations. Sheppard, 
W. F. L. Mth. S. P. 31 (1900) 70-. 

researches in the Netherlands. Quetelet, 
L. A. J. Brux. Ac. Sc. Mm. 5 (1829) 
vi + 57 pp. 

science, new step in. Gallon, F. Nt. 51 
(1894-95) 319. 

study on recruiting for the Polytechnic 
School. Montessus de Bailor e, F. de. Par. 
EC. Pol. J. 63 (1893) 27-. 

tables, errors of the argument. Kleiber, J. 

B. A. Ep. (1888) 618. 

, probability of uniformity. Campbell, E. 

Ph. Mg. 18 (1859) 359-. 
Statistics. Wittstein, T. D. Nf. B. 40 (1865) 

112-. 

. Geddes, P. Nt. 24 (1881) 523-. 
, application of binomial law. Brown, S. 

I. Act. J. 17 (*1873) 340-. 
, association of attributes. Yule, G. U. [1899] 

Phil. Trans. (A) 194 (1900) 257-. 
, Bengal. Bedford, J. JR. Beng. As. S. J. 

22 (1853) 387-. 
, Camborne. Lanyon, E. Cornwall Pol. S. 

T. (1841) 99-. 
, classification. Geddes, P. [1881] Edinb. 

E. S. P. 11 (1882) 295-. 

of conditions of life among working classes. 
Bodio, L. Em. E. Ac. Line. T. 6 (1882) 
317-. 

, correction of some documents. Demon- 
ferrand, F. Par. EC. Pol. J. 16 (27 e cah.) 
(1839) 75-. 

of effect of cholera, 1832 and 1849. Dupin, C. 

C. E. 34 (1852) 65-. 

Egypt, 1837. Duhamel, A. Es. Gg. Gs. 

D. 1 (1849) 93-. 

, formula for reduction. Enestrom,G. Stockh. 
Ofv. (1893) 397-; Fschr. Mth. (1893-94) 
359-. 

of fuels. Morville, N. [1798] Kiob. Dn. 
Vd. Selsk. Skr. 1 (1800) 205-. 

general, of different countries. Quetelet, 
L.A.J. Brux. Ac. Bll. 12 (1861) 99-. 

, judiciary. Liouville, E. Liouv. J. Mth. 
18 (1873) 145-. 

and last census, British Empire. Merritt, 
. QJ. Sc. 2 (1827) 283-. 

, Lot (dept.). Cordier,L. J. Mines 21 (1807) 

445-; 22(1807)5-. 
, mathematical. Ktittner, W. Z. Mth. Ps. 

25 (1880) 11-; 26 (1881) 297-; 32 (1887) 



1635 



Statistics, States of the world. Babbi, A. 

Mil. G. I. Lomb. 3 (1842) 387-. 
, use. Delauney, . C. E. 108 (1889) 

909-. 
Still-born children, estimation of number. 

Demonferrand, F. C. E. 3 (1836) 615-. 
Suicide in Finland. Westerlund, F. W. Hel- 

singf. Bd. 58 (1900) 111-. 
, statistics. Jopling, R. T. Assur. Mg. [1 

(*1851)] 308- ; 2 (1852) 32-. 
Summation, approximate, of numerical tables. 

Buniakovskij, V. Ja. [1867] St Pet. Ac. Sc. 

Mm. (Es.) 12 (1868) (Suppl.) No. 4, 41 pp. 
Sums of drawings, final law. De Morgan, A. 

I. Act. J. 14 (*1869) 175- . 
Surplus, conditions giving rise to. Jellicoe, C. 

Assur. Mg. 2 (*1852) 333-. 

determination. Gill, C. Assur. Mg. [1 
(*1851)] 357-. 

. Younger, S. Assur. Mg. 4 (*1854) 

249-. 
and distribution. M . , A . (Editor.) Assur. 

Mg. [1 (*1851)] 22 bis-, 159-, 359-. 

, certain objectionable methods. 
Jellicoe, C. Assur. Mg. 3 (*1853) 185-. 

distribution. Romans, S. Assur. Mg. 11 
(*1864) 121-. 

. Manly, H. W. I. Act. J. 23 (M882) 

233-. 
. Lidstone, G. J. I. Act. J. 32 (1896) 

73-. 

, as defeating object of life assurance. 
Terry, J. Assur. Mg. 10 (*1863) 130-. 

, methods. Sprague, T. B. Assur. Mg. 

6 (*1857) 290- , 344-; 7 (*1858) 61-. 

, , various. Pattison, W. P. Assur. 

Mg. 9 (*1861) 341-. 

, formula for returning to assured their con- 
tributions. Harvey, C. J. I. Act. J. 24 
(1884) 173-. 

premiums and interest, bonuses arising from. 
Sunderland, A. W. I. Act. J. 26 (1887) 
357-. 

Surrender of policies, allowance. Jellicoe, C, 

Assur. Mg. [1 (*1851)] 279-. 
, . Crisford, G. S. I. Act. J. 21 

(*1879) 301-. 

values, solution of problem. Marr, T. I. 
Act. J. 14 (*1869) 156-. 

, and their calculation. Fulford, F. W. 

I. Act. J. 35 (1901) 199-. 
Survivorship annuities, calculation by columnar 

method. Meikle, J. Assur. Mg. 11 (*1864) 

40-. 

assurance tables, construction. Gray, P. 
Assur. Mg. 5 (*1855) 107-. 

premiums, calculation. Sunderland, A. W. 
I. Act. J. 27 (1889) 509-. 

between two lives, probabilities. Gray, P. 
Assur. Mg. [1 (*1851)] 137-. 

, . Ackland, T. G. I. Act. J. 

27 (1889) 157-. 

, , method for computing. 
Chisholm, D. Assur. Mg. 2 (*1852) 305-. 

Survivorships, general problems concerning. 

Makeham, W. M. Assur. Mg. 12 (*1866) 61-. 
, three life. Makeham, W. M. Assur. Mg. 

12 (*1866) 118-. 



120 



1635 Theory of Statistics, etc. Calculus of Differences, etc. 1640 



Symbol d x , origin. Cherriman, J. B. I. Act. 
J. 21 (*1879) 295-. 

Taxation of temporary versus perpetual an- 
nuities. Hardy, P, Assur. Mg. 3 (*1853) 
195-. 

and wealth, relation between. Gobbi, U. 
Mil. I. Lomb. Kd. 32 (1899) 756-. 

Taxes, principles regulating incidence. Jenkin, 

F. Edinb. B. S. P. 7 (1872) 618. 
Ten year non-forfeiture policies. Younger, S. 

I. Act. J. 14 (*1869) 476-; 15 (*1870) 

151-. 
, American. Cherriman, J. B. 

I. Act. J. 16 (*1872) 384-. 
, . McClintock, E. I. Act. J. 

17 (*1873) 301-. 
Term assurance, life against life, value. Smith, 

H. A. Assur. Mg. 9 (*1861) 295. 
for two joint lives. Otter, W. C. Assur. 

Mg. 8 (*1860) 113-. 
Terms of imprisonment, statistics and curves. 

Gallon, F. Nt. 52 (1895) 174-. 
Tontine, American, and mutual assessment 

schemes. Manly, H. W. I. Act. J. 26 (1887) 

182-. 
, perpetual. Navier, C. L. M. H. A. C. 12 

(1819) 103-. 
Tontines, early history. Hendriks, F. Assur. 

Mg. 10 (*1863) 205-. 
Two life assurances, extra premiums in respect 

of. Ryan, G. H. I. Act. J. 24 (1884) 305-. 
Under-average lives, treatment of. Sunderland, 

A. W. I. Act. J. 29 (1892) 419-. 
Uniform mortality law from birth to old age. 

Gompertz, B. I. Act. J. 16 (1872) 329-. 

seniority, law. Henderson, R. I. Act. J. 
32 (1896) 293-. 

United States, eighth census. Brown, S. Assur. 

Mg. 13 (* 1867) 226-. 
, formula for predicting population. Prit- 

chett, H. S. St Louis Ac. T. 5 (1892) 599-. 
Universal notation , necessity for a. Begault, A . 

I. Act. J. 33 (1898) 1-. 
Utility, theory. Gobbi, U. Mil. I. Lomb. Bd. 

81 (1898) 237-, 325-, 1300-. 
Vaccination, longevity in France before and 

after its introduction. Dupin, C. C. B. 27 

(1848) 565-. 

and small pox, statistics. Sprague, T. B. 
I. Act. J. 20 (*1878) 2 16-. 

Valuation of absolute reversions. Mount- 
castle, H. I. Act. J. 15 (*1870) 148-. 

, certain methods. Gray, W. T. I. Act. J. 
20 (*1878) 309-. 

methods, notes. Dovey, W. R. I. Act. J. 

34 (1899) 346-. 

producing definite reserve. Hardy, JR. P. 
I. Act. J. 1 (1895) 325-. 

reserves, approximate calculation. Chis- 
holm, J. I. Act. J. 27 (1889) 442-. 

returns, with reference to Life Assurance 
Companies Act. Todhunter, R. I. Act. J. 

35 (1901) 1-. 

of whole term policies, tables. Hume, A. S., 
(& Stott, W. I. Act. J. 34 (1899) 396-. 

Value of benefits, on principle of collective 
assurance. Hardy, R. P. I. Act. J. 30 
(1893) 79-. 



Value of contingent reversion under certain 

limitations. Hardy, P. Assur. Mg. 2 

(*1852) 91-, 298. 
options. Stephewon, J. W. Assur. Mg. 

12 (*1866) 302-. 
. Younger, S. Assur. Mg. 13 (*1867) 

55. 
. Gray, P. Assur. Mg. 13 (*1867) 

104-. 
. Younger, S. Assur. Mg. 13 (*1867) 

118. 
, Stephenson's theory. Makeham, W. M. 

Assur. Mg. 12 (*1866) 363-. 
, . Smith, H. A. Assur. Mg. 13 

(*1867) 103. 

and prices, mathematical investigations. 
Fisher, I. Conn. Ac. T. 9 (1892-95) 1-. 

of property and conditions which determine 
it. Buquoy, G. von. Oken Isis (1824) 28-. 

reversions payable at instant of death. 

Chisholm, D. Assur. Mg. 4 (*1854) 70-. 
selection as exercised by policy holder. 

Higham, J. A. .Assur. Mg. [1 (*1851)] 179-. 
Values, elementary, special arrangement. 

Oakes, W. H. Assur. Mg. 12 (*1866) 57-. 
Vital statistics ; geometric mean. Gallon, F. 

B. S. P. 29 (1879) 365-. 
of Glasgow, 1869 and 1870. Scott, A. 

Glasg. Ph. S. P. 8 (1873) 78-. 
Society of Friends. Fryer, A. Manch. 

Ph. S. Mm. 14 (1857) 153-. 
towns in Scotland. Sykes, W. H. 

B. A. Bp. (1842) 121-. 
Wealth, social, mathematical theory. Walrus, 

L. [1876] Laus. S. Vd. Bll. 14 (1877) 365-, 

525-. 
Whole-life assurance business, approximate 

valuation. Woolhouse, W. S. B. I. Act. J. 

27 (1889) 433-. 

assurances, a certain conversion of. 
M., T. Assur. Mg. 13 (*1867) 246-. 

time assurances on single lives, valuation. 
Coles, J. Assur. Mg. 7 (*1858) 179-. 

Widows' pensions, statistics. Enestrom, G. 
Stockh. Ofv. (1894) 479-; Fschr. Mth. 
(1893-94) 363-. 

and spinsters, marriage rates. Sprague, T. B. 
I. Act. J. 22 (*181) 352-. 

Yearly into fractional yearly payment, trans- 
formation. McKenzie, D. J. McG. I. Act. 
J. 23 (*1882) 162-. 



1640 Calculus of differences ; 
interpolation. 

Adjunct of a given linear finite difference form. 

Bortolotti, E. Em. B. Ac. Line. Bd. 5 

(1896) (Sem. 1) 349-. 
Algebra of difference-tables. Everett, J. D. 

QJ. Mth. 31 (1900) 357-. 
Approximate summation, formulae. Hardy, 

G. F. I. Act. J. 24 (1884) 95-. 
of series. Korteweg, D. J. N. Arch. 

Wisk. 2 (*1876) 161-. 
Approximation methods of former times. Giin- 

ther, S. D. Nf. B. (*1877) 95-. 



121 



Calculus of Differences ; Interpolation 



1640 



Boole's finite differences, notation. Wilding, E. 

I. Act. J. 22 (*1881) 60-. 
Calculus of differences, algebraic transformation 

by. Cesdro, E. N. A. Mth. 5 (1886) 489-. 
, finite and infinitesimal. Gregory, 

D. F. Camb. Mth. J. 1 (1339) 212-. 
, point in. Tisserand, F. C. E. 70 

(1870) 678-. 
, theorem. Hamilton, (Sir) W. E. 

B. A. Ep. (1843) (pt. 2) 2-. 

enlargement (extension of calculus of 
finite differences). MeClintock, E. Am. J. 
Mth. 2 (1879) 101 -. 

, theorems. MeClintock, E. Am. J. 

Mth. 17 (1895) 69-. 
functions derived from limiting ratios. 

Echols, W. H. [1395] A. Mth. 10 (1895-96) 

50-. 
generating functions. L., E. J. Camb. 

Mth. J. 2 (1841) 94-. 
Central-difference formulas. Sheppard, W. F. 

[1399] L. Mth. S. P. 31 (1900) 449-. 
interpolation formula* Everett, J. D. 

B. A. Ep. (1900) 648-. 

formulas. Spencer, J. I. Act. J. 
33 (1898) 349-. 

Constant coefficients in finite differences, theory. 

Naylor, J. I. Act. J. 23 (*1382) 420-. 
Convergents applied to Cauchy's interpolation 

fractions. Pade, H. C. E. 130 (1900) 697-. 
Cotes' numbers, calculation by approximate 

quadratures. Blazek, G. Prag Sb. (1879) 

167-. 
Cotton spinning problem. Woolhouse, W. S. B. 

Assur. Mg. 11 (*1364) 224-. 
Cyclical equations, connection with method of 

least squares. Nekrasov, P. A. Eec. Mth. 

(Moscou) 12 (1385) 377-. 
Deduction of increase rates from tables. Everett, 

J. D. Nt. 60 (1899) 271. 
. Eunge, C. Nt. 60 (1399) 

365-. 
A m O n applied to integration. Herapath, J. 

Tilloch Ph. Mg. 65 (1325) 321-. 
and Hargreave's form of it. Sums of 

powers of numbers etc. Scott, G. [1865] 

QJ. Mth. 8 (1867) 21-. 
Determination of functions from special values 

of variable. Chebuishev, P. L. (xn) [1369] 

Eec. Mth. (Moscou) 4 (1369-70) (Pt. 1) 231-. 
Difference, ith, deduced from nth differential. 

Picart, A. N. A. Mth. 12 (1373) 413-. 
Differences and differential coefficients, con- 
nexion between. Nielsen, H. P. N. Ts. 

Mth. 8 (B) (1397) 86-; Fschr. Mth. (1897)246. 
differentials of functions of zero. Hamilton, 

(Sir) W. E. [1831] Ir. Ac. T. 17 (1337) 235-. 
nth order. Spitzer, S. Grunert 

Arch. 33 (1359) 115-. 

method, application to series summed by 
help of impossible quantities. Gompertz, B. 
Phil. Trans. (1806) 174-. 

, construction of tables by. Gray, P. 

Assur. M ? . 13 (*1367) 61-, 149-, 293-; I. 

Act. J. 14 (*1869) 307-. 
, , 2 theorems. Knight, T. Phil. Trans. 

(1317) 234-. 
,mth,ofO. Scott, G. QJ. Mth. 5 (1362) 323-. 



1640 



Differences, relation between various orders. 

Harvey, G. Thomson A. Ph. 7 (1816) 475-. 
, series of, theory. Werner, 0. Grunert 

Arch. 23 (1354) 231- ; 24 (1855) 90-. 
, , . Wallentin, I. G. Arch. Mth. 

Ps. 63 (1879) 56-. 

and Taylor's theorem. Adams, Jas. Thom- 
son A. Ph. 11 (1818) 275. 

, theory. Sharpe, S. Ph. Mg. 19 (1831) 137-. 

of 0. Alberti, V. G. Mt. 38 (1900) 11 1-. 
Differentiation by aid of finite differences and 

vice-versa. Lobatto, E. Crelle J. 16 (1837) 
11-. 

, arithmetical. Philippoic, M. M. Fschr. 
Mth. (1899) 267. 

under sign of integration, extension to finite 
differences, with applications. Chio, F. Tor. 
At. Ac. Sc. 6 (1870-71) 194-. 

Empirical formulae. Kleiber, I. A. Es. Ps.-C. 

S. J. 22 (Ps.) (1890) 11-; J. de Ps. 10 (1891) 

433-. 
, comparison. Runge, C. Z. Mbh. Ps. 

45 (1900) 78-. 
Equation of finite differences, giving sums and 

differences of Ex. Gaudin, (Col.) . Les 

Mondes 3 (1863) 567-. 
Equations, algebraic, theorems. Mathieu, E. 

N. A. Mth. 15 (1856) 409-. 

of differences for approximating to differential 
equation. Coriolis, G. Liouv. J. Mih. 2 
(1837) 230-. 

Error of linear interpolation. Bary, . Ger- 

gonne A. Mih. 21 (1830-31) 281-. 
Errors by interpolation from logarithmic and 

other tables. Woodward, E. S. A. Mth. 2 

(1885-86) 54-. 
, logarithmic. Howe, H. A. A. Mth. 1 

(1884-85) 126- ; 2 (1885-86) 39-, 77-; 3 

(1887) 74. 
, theory, formula in. Makeham, W. M. 

I. Act. J. 28 (1890) 393-. 
Euler's summation formula. Landre, C. L. 

N. Arch. Wisk. 6 (*1880) 212-. 
Exponential functions and finite differences. 

Herschel, (Sir) J. F. W. [1815] Phil. Trans. 

(1816) 25-. 
Factorial notation. Elphinstone, H. W. QJ. 

Mth. 2 (1858) 122-, 254-. 
Faculties expressed by A m O n . Jeffery, H. M. 

QJ. Mth. 4 (1861) 364-. 
Figurate numbers and interpolation, short proofs 

of theorems. Soufflet, . Les Mandes 13 

(1867) 336-. 

series. Smyth, B. B. Kan. Ac. Sc. T. 14 
(1896) 29-. 

Finite difference equations, partial. Paoli, P. 

Mod. S. It. Mm. 8 (1794) 575-. 
integrals expressed by definite integrals. 

Tortolini, B. Tortolini A. 4 (1853) 209-. 

differences calculus. Eussell, W. H. L. 
M3ss. Mth. 11 (1882) 33-. 

applied to definite integrals. Paoli, P. 

Mod. S. It. Mm. 20 (1828) 255-. 
, A n (x m ), factor in general term of. 

Kohlau, E. Crelle J. 6 (1830) 255-. 
, determinants of functions in the. 

Bortolotti, E. Em. E. Ac. Line. Ed. 5 (1896) 

(Sem. 1) 254-. 



122 



1640 Calculus of Differences, etc. 

Finite differences calculus, formula in. Carr, 
T. I. Act. J. 14 (* 1869) 479-. 



Malmsten, C. J. Stockh. Ak. Hndl. (1844) 

363-; Crelle J. 35 (1847) 55-. 
--- , formulae. Tortolini, P. A. Mt. 5 

(1863) 181-. 
--- , , useful. Hill, G. W. Des MMnes 

Anal. 1 (1874) 141-. 
--- , methods. Carmichael, R. NH. Ev. 

7 (1360) (P.) 78-, 170-. 
--- -, theorem, new. Booth, J. Ph. Mg. 

19 (1841) 125-. 

, theorems, new, based chiefly on re- 

searches on complex variability. Casorati, F. 

A. Mt. 10 (1880-82) 10-. 
-- , and theory of numbers, contribution 

to. Busche, E. Mth. A. 53 (1900) 243-. 
-- , direct method. Adams, Jas. Thomson 

A. Ph. 16 (1820) 281-. 
-- , formula. Cayley, A. QJ. Mth. 2 (1858) 

198-. 
-- , formulae. Cauchy, A. L. C. E. 19 

(1344) 1179-. 
-- , integrals. Cauchy, A. L. C. E. 39 

(1854) 21 i-. 
-- , . Bmmiakowtky, V. St Pet. Ac. Sc. 



Mm. 1 (1859) No. 9, 13 pp. 
, E. Les 
701-. 



-- , . Barbier, 



Mondes 3 (1863) 



-- , . Thoman,F. C. E. 57 (1863) 778-. 
-- of powers, conversion to definite integrals. 

Cauchy, A. L. [1815] Par. EC. Pol. J. 17 

(28 cah.) (1841) 147-. 
-- , return to original series from nth term of 

with series of differences. Mtiller, G. W. 

Grunert Arch. 1 (1341) 211-. 

, series connected with. Lukas, F. C. 
Wien Az. 32 (1395) 269-. 

-- , and Taylor's series. Carvallo, E. N. A. 
Mth. 10 (1391) 24-. 

or mixed differences, uestions depending 
on. Combescure, E. Par. EC. Norm. A. 
3 (1874) 305-. 

Forms A" O x and congeners. Horner, J. QJ. 

Mth. 4 (1861) 111-, 204-. 
Formula for A0 i / i when and i are very large 

numbers. Cayley, A. [1387] Edinb. E. S. P. 

li (1388) 119-. 
Functions, approximate forms for representa- 

tion. Pincherle, S. Bologna Ac. Sc. Mm. 

10 (1889) 77-. 
Harmonic series, representation by sequences 

of factors. Eogel, F. Arch. Mth. Ps. 9 

(1890) 297-. 
Illusory interpolations, new examples. Meray, 

C. Ell. Sc. Mih. 20 (1396) 266-. 
Indeterminate analysis, application of calculus 

of finite differences. Piola, G. A. Sc. Lomb. 

Ven. 1 (1831) 101- ; Tortolini A. 1 (1350) 263-. 
Integrability of differential and finite difference 

equations, conditions. Mmich, S. R. Tor- 

tolini A. 1 (1350) 321-. 
Integral, finite, 2 n #a; expressed as a definite 

integral. Abel, N. H. Mg. Ntvd. 6 (1325) 

182-. 



Interpolation 1640 

Integral, finite, 2e*7/. Malmsten, C. J. Ups. 

N. Acta S. Sc. 12 (1844) 293-. 
Integration of difference equations reducible to 

linear form. Oltramare, G. As. Fr. C. E. 

(1893) (Pt. 2) 106-. 

in finite differences. Trembley, J. Berl. 
Mm. Ac. (1799-1300) 18-. 

of linear difference-equations. Oltramare, G. 
As. Fr. C. E. (1891) (Pt. 2) 66-; (1895) 
(Pt. 2) 175-. 

, use in arithmetical calculations. Cesdro, 
E. Palermo Cir. Mt. Ed. 1 (1387) 293-. 

Interpolated multiples. Soule, . Bordeaux 
S. Sc. Mm. 4 (1894) iii-. 

Interpolating functions. Cauchy, A. L. C. E. 
11 (1840) 775-. 

. Genocchi, A. Tor. Ac. Sc. At. 13 

(1877) 716- ; 15 (1880) 269-; C. E. 86 

(1878) 466-. 

. Peano, G. Tor. Ac. Sc. At. 18 (1882) 

573-. 

, elementary proof of a fundamental 
property. Schwarz, C. H. A. Tor. Ac. Sc. 
At. 17 (1381) 740-. 

INTEEPOLATION. 

Legendre, A. M. Con. des Temps (1819) 

302-. 

Degen, C. F. As. Nr. 1 (1823) 231-. 
Clausen, T. Crelle J. 5 (1829) 305-. 
Encke, J. F. Berl. As. Jb. (1830) 265-. 
Cauchy, A. L. [1835] Mod. Mm. S. It. 21 

(1836) 374-. 

Biot, J. B. C. E. 13 (1344) 545. 
Brassinne, E. Liouv. J. Mth. 11 (1846) 

177-. 
Cauchy, A. L. Con. des Temps (1852) 129- ; 

C. E. 37 (1853) 64-. 

Lehmann, J. W. H. As. Nr. 39 (1855) 257-. 
Grunert, J. A. Grunert Arch. 32 (1859) H9-. 
Hermite, C. C. E. 48 (1359) 62-. 
Rouche, E. N. A. Mth. 13 (1859) 26-. 
Cebysev, P. St Pet. Ac. Sc. Mn. (Rs.) 4 

(* 1864) (Suppl.) No. 5, 23 pp. 
Tisserand, F. C. E. 68 (1869) 1101-. 
Nell, A. M. Arch. Mth. Ps. 61 (1877) 135-. 
Bartl, C. [1877] Arch. Mth. Ps. 62 (1378) 

202-. 
Laisant, C. A. As. Fr. C. E. (1891) (Pt. 2) 

222-. 
Pincherle, S. Bologna Ac. Sc. Maa. 3 (1392) 

293-. 

Borel, E. C. E. 124 (1397) 673-. 
Laisant, . As. Fr. C. E. (1897) (Pt. 2) 86-. 
Markov, A. St Pet. Ac. Sc. Mm. 6 (1398) 

No. 5, 69 pp. ; Fschr. Mih. (1898) 252-. 
Veltmann, W. Z. Mth. Ps. 44 (1899) 303- ; 45 

(1900) 337. 
and application to cubic equations. Vieille, J. 

N. A. Mth. 10 (1851) 48-. 
applied to extraction of square and cube roots. 

Dolguschin, P. A. Fschr. Mth. (1898) 139. 
approximate. Bellavitis, G. Ven. At. (1858- 

59) 1109-. 
fractions. Gyory, S. (xn) Mag. Ak. Ets. 

(1854) 165-. 



123 



1640 Interpolation 



Interpolation 1640 



astronomical formulae. Le Verrier, U. J. J. 
(x) Par. Obs. A. 1 (1855) 73-; 2 (1856) 
301+ [167] pp. ; 3 (1857) 199-, and [1]- ; 4 
(1858) 1-, and [1]-; 5 (1859) 1- ; 6 (1861) 
435pp.; 10 (1874) 1-, and [1]-; 11(1876) 
560+ [136] pp. ; 12 (1876) 76+ [178] +A. 80 
+ [A. 286] pp. ; 13 (1876) 1-, and [1]- ; 14 
(1877) Pt. 1, A. 1-, and [A. 1]-; Pt. 2, 1-, 
and [1]-. 

and Bernoulli's numbers. Lipschitz, R. 0. S. 
C. E. 86 (1878) 119-. 

Briggs' Log. Tables. Legendre, A. M. Con. 
des Temps (1817) 219-. 

and calculus of differences finite or infinite, 
principles. Ampere, A. M. Gergonne A. 
Mth. 16 (1825-26) 329-. 

certain forms. Bartlett, W. P. G, Bost. Mm. 
Am. Ac. 8 (1863) 435-. 

chemical and physical observations. Bartlett, 
W. P. G. Silliman J. 34 (1862) 27-. 

choice of best ordinate. Kleiber, I. A, Kazan 
S. Nt. (Ps.-Mth.) P. 8(1890) 232-; Fschr. 
Ps. (1890) (Ab. 1) 13. 

by circular functions. Gomes Teixeira, F. N. 
A. Mth. 4 (1885) 351-. 

curves of 3rd and 5th order. Dupin, C. 
C. E. 25 (1847) 769-. 

differences. Burckhardt, J. K. Zach M. 
Cor. 12 (1805) 332-. 

at equidistant values. Cebysev, P. St Pet. 

Ac. Sc. Mm. (Rs.) 25 (*' 1874-75) (Suppl.) 

No. 5, 30 pp. 
formula. Tchebicheff, P. [1854] St Pet. Ac. 

Sc. fill. 13 (1855) 210-. 

. Brioschi, F. Tortolini A. 2 (1859) 
132-. 

. Gomes-Teixeira, F. Liege S. Sc. Mm. 10 
(1883) (No. 10) 7 pp. 

, Cauchy. Schott, C. A. U. S. Coast Sv. 
Ep. (1860) 392-. 

, Gauss, infinitely extended. Bendixson, I. 
Acta Mth. 9 (1887) 1-. 

, Hermite, expressed algebraically. Schering, 
E. C. E. 92 (1881) 510-. 

, Lagrange. Dirksen, E. H. Crelle J. 1 
(1826) 22 1-. 

, . Gamier, J. G. Brux. Ac. Bll. 6 
(1839) (pte. 2) 19-. 

, . StudnicJca, F. J. Casopis 2 (* 1873) 
82-; Fschr. Mth. (1873) 122-. 

, . Hermite, C. [1877] Crelle J. Mth. 
84 (1878) 70-. 

, . Stieltjes, T. J. (jun.\. [1881] Amst. 
Ak. Vs. M. 17 (1882) 239-. 

, . Bendixson, I. C. E. 101 (1885) 1050-, 
1129-. 

, . Echols, W. H. A. Mth. 8 (1893-94) 
22-. 

, . Lewicki, W. Wiad. Mt. 3 (1899) 
264-; Fschr. Mth. (1899) 244. 

. , generalisation. Williot, V. Bll. Sc. 
Mth. 14 (1890) 218-. 

. , remainder in. Sonin, N. J. Fschr. 
Mth. (1899) 242. 

, (mortality-tables). Selling, E. Crelle J. 
Mth. 106 (1890) 193-. 

, new. Alexander, J. H. Silliman J 7 
(1849) 14-. 



formula, Newton. Oppermann, L. I. Act. J. 

15 (*1870) 145-, 177-. 
, . Jensen, J. L. W. V. Kjrfb. Ov. (1894) 

246-. 
, Pictet. SzUy, K. [1879] J. de Ps. 9 

(1880) 303-. 
, Prony. Minich, S. R. Ven. At. 13 (1867- 

68) 1153-. 
, Tchebicheff's (Cebysev). Tchebicheff, P. 

N. A. Mth. 18 (1859) 193-. 
formulae. Ferrel, W. [1865] Am. Ac. P. 7 

(1868) 2-. 

. Carvallo, J. C. E. 106 (1888) 346-. 
. Radau, R. Bll. As. 8 (1891) 273-, 325-, 

376-, 425-. 
, application. Ackland, T. G. I. Act. J. 32 

(1896) 286-. 

and application to solution of equations. 
Olivier, L. Crelle J. 2 (1827) 197-. 

for functions of several variables. Kronecker, 
L. Berl. Mb. (1865) 686-. 

, Gauss, for n=7, 8 and 9. Perott, J. QJ. 

Mth. 25 (1891) 200-. 
, Hansen. Mollweide, C. As. Nr. 2 (1824) 

259-. 
, Lagrange. Lewicky, W. Arch. Mth. Ps. 

17 (1900) 214-. 
, , generalised, applications. Puzyna, J. 

Krk. Ak. (Mt.-Prz.) Pam. 14 (1888) 1-; 

Fschr. Mth. (1888) 251-. 
, and Newton. Gerono, G. C. N. A. 

Mth. 16 (1857) 317-, 358-. 
, . Transon, A. (Prof.). N. A. 

Mth. 19 (I860) 248-. 
, new. Astrand,J.J. ChristianiaF. (1890) 

(Ov.) 5-. 
, various. Cauchy, A. L. C. E. 12 (1841) 

283-. 
by fractional rational function. Jacobi, C. G. J. 

Crelle J. 30 (1846) 127-. 

functions of a variable. Sarrus, F. (vi 
Adds.) Strasb. S. Sc. N. Mm. 2 (1832) 
203-. 

in heat. Bary, E. C. E. 3 (1836) 378. 

of implicit functions, and calculation of roots. 

Maksimovich, V. P. (xn) [1881] Kazan 

S. Nt. (Ps.-Mth.) P. 1 (1883) [No. 5] 

(Suppl.) 23 pp. 
and integration in series. Buchwaldt, F. Ts. 

Mth. 5 (1887) 79-, 97-; Fschr. Mth. (1887) 

281-. 
of irrational and logarithmic functions by 

numerical tables. Lefort, P. A. F. [1857] 

Edinb. E. S. P. 8 (1875) 602-. 
inverse. Siebdrat, (Dr.). Dresden Sb. Isis 

(1871) 233-. 
kinematic. Laisant, C. A. As. Fr. C. E. 

(1890) (Pt. 2) 70-. 
Lagrange's theorem, generalisation. Sylvester, 

J. J. Ph. Mg. 6 (1853) 374-. 
by least squares. Gergonne, J. D. Gergonne 

A. Mth. 6 (1815-16) 242-. 

. Ceby'sev, P. L. (Tchebicheff). 
St Pet. Ac. Sc. Mm. 1 (1859) No. 15, 
24 pp. 

. Borchardt, C. W. [1860] Crelle J. 

58 (1861) 270-. 



124 



1640 Interpolation 

by least squares, formulae. CebySev, P. L. 

(Chebuishev). (xn) Bee. Mth. (Moscou) 3 

1868) (Ft. 1) 157-. 
, (Tchebychef). Schols, C. M. 

[1375] Amst. Ak. Vs. M. 9 (1876) 301- ; 

Arch. Neerl. 12 (1877) 102-. 
and new method, comparison. Cauchy, 

A. L. C. B. 37 (1853) 100-. , 
legitimacy. Meray, C. Par. EC. Norm. A. 1 

(1884) 165-. 
as means of calculating irrationals. Opper- 

mann, L. Kjob. Ov. (1375) 18-. 
and mechanical quadrature. Grunert, J. A. 

Grunert Arch. 20 (1853) 361-. 
quadratures in astronomy. Santini, G. 

Yen. Mm. I. 13 (1S66) 177-. 
method. Uylenbroek, P. J. Leijd. A. Ac. 

(1820-21) 77 pp. 
, Cauchy. Grunert, J. A. Grunert Arch. 2 

(1342) 41-. 

, . Seeliger, H. As. Nr. 96 (1880) 235-. 
, , modified by method of least squares. 

Despeyrous, C. Toul. Mm. Ac. 5 (1867) 251-. 
, general. Buquoy, G. von. Oken Isis 

(1827) 889-. 
, geometrical. Genge, C. Ziir. Vjschr. 31 

(1886) 268-. 
, new. Astrand, J. J. Leip. As. Gs. Vjschr. 

10 (1875) 279-. 
, general. McGlintock, E. Am. J. Mth. 

2 (1879) 307-. 
, Tschebyschew. Backlund, 0. St Pet. Ac. 

Sc. Bll. 29 (1384) 477-. 
methods. Le Verrier, U. J. J. (vi Adds.) 

Par. A. Obs. 1 (1855) 73-; 2 (1856) 1-; 3 

(1857) 199- ; 4 (1358) 1- ; 5 (1359) 1-; 6 
1861).!-. 
, special. Niven, W. D. [1377] Mess. Mth. 

7 (1878) 35-. 

mixed. Cousinery, B. E. Ing. 1 (1848) 125-. 
new formula. Sprague, T. B. I. Act. J. 22 

(* 1881)270-. 
between observed values. Tchebiche/, P. St 

Pet. Ac. Sc. Bll. 16 (1858) 353- ; St Pet. Ac. 

Sc. Mm. 1 (1859) No. 5, 81 pp. 
by parabolic curve. Michal, A. C. B. 37 

(1853) 185-. 
curves. Michal, A. A. Pon. Chauss. 10 

(1865) 59-. 
parabolic, by least squares method. Degen, 

C. F. [1823] St Pet. Mm. Sav. 6tr. 1 (1831) 

12-. 
, . Grave, P. Kazan S. Nt. 

(Ps.-Mth.) P. 7 (1889) 270- ; Fschr. Mth. 

(1889) 220. 
periodic functions. Weyer, G. D. E. Leip. 

As. Gs. Vjschr. 22 (1887) 292-. 
philosophy. Gergonne, J. D. Gergonne A. 

Mth. 5 (1814-15) 252-. 
in physics. Mollweide, C. Gilbert A. 62 

(1819) 422-. 
problem. Korkine, A. Bll. Se. Mth. As. 6 

(1882) 228-. 

. Badau, R. Bll. As. 4 (1887) 515-. 
. Bohlmann, G. Gott. Nr. (1899) 260-. 
. Pincherle, S. Palermo Cir. Mt. Bd. 14 

(1900) 142-. 



Calculus of Differences, etc. 1640 

Interpolation, continued. 

problem, Cauchy. Netto, E. Mth. A. 42 

(1893) 453-. 
, general. Greatheed, S. S. (vi Adds.) 

Camb. Mth. J. 3 (1843) 97-. 
problems, mechanical solution. Jung, G. Mil. 

I. Lomb Bd. 13 (1380) 226-. 
proof of formula. Berridge, G. W. I. Act. J. 

14 ( 1869) 244-. 
with proofs of methods of Briggs, Mouton, and 

Newton. Maurice, F. Con. des Temps 

(1847) 181-. 
questions of fluid motion. Barre de Saint- 

Venant, . C. B. 17 (1343) 1108-. 
recurring series. Maillet, E. N. A. Mth. 14 

(1395) 473-. 

with reference to development and differentia- 
tion. Roberts, S. [1865] QJ. Mth. 7 (1866) 

184- ; 8(1867)52-, 139-. 
results. Thiele, T. N. (xn) Ts. Mth. 1 (1883) 

183- ; Fschr. Mth. (1884) 198-. 
to second order without change of sign. Airy, 

(Sir) G. B. As. S. M. Not. 26 (1866) 236-. 
series. Bangma, 0. S.,(& J. F. Keyser. Amst. 

Mengelwerk 2 (1316) 42-. 
A v A,A 2 ,...A 1 A n A 3 ...A n . Svanberg, A. F. 

Stockh. Ak. Hndl. (1828) 1-. 
in statistics. Westergaard, H. I. Act. J. 32 

(1896) 276-. 
by successive differences, exactness. Mollweide, 

C. Zach M. Cor. 21 (1810) 331-. 
summation and adjustment of tables. Wool- 
house, W. S. B. Assur. Mg. 11 (*1864) 61-, 

301- ; 12 (*1866) 136-. 
and summation of numerical series, method. 

Donald, J. Glasg. Ph. S. P. 9 (1875) 272-. 
symmetric function. Borchardt, C. W. Berl. 

Ab. (1860) (Mth.) 1-. 
table, general. Amante, F. (xn) [1844] Nap. 

Ac. Pont. At. 4 (1351) 251-. 
tables. Heawood, P. J. Mess. Mth. 27 (1898) 

121-. 
, adequacy. Jelinek, V. Casopis 21 (1892) 

31- ; Fschr. Mth. (1392) 227. 
theorem of Hermite. Gomes-Teixeira, F. 

Crelle J. Mth. 100 (1887) 83-. 
theory. Lerch, M. Prag Ceske Ak. Fr. Jos. 

Bz. (Trida 2) 1 (1892) Art. 32, 15 pp. ; 

Fschr. Mth. (1892) 227. 
. loachimescu, A. G. Bucarest S. Sc. Bll. 

6 (1897) 472-. 
of values depending on two variables. Seydler, 

A. Prag Sb. (1889) 2 (Mth.-Nt.) 337-; 

Fschr. Mth. (1889) 253-. 



Inverse calculus of differences, formula. 

Prouhet, E. N. A. Mth. 10 (1851) 186-. 
, notes. Combescure, E. C. B. 74 

(1872) 454-. 
method of finite differences. Brinkley, J. 

Phil. Trans. (1807) 114-. 
Least squares method, case where number of 

unknowns is large. Nekrasov, P. A. Bee. 

Mth. (Moscou) 12 (1885) 189-. 
Legendre's functions, use of, for interpolation. 

Seeliger, H. Munch. Ak. Sb. 20 (1891) 499-. 



125 



1640 Calculus of Differences, etc. 

Linear difference forms with commutative 

factors of prime degree. Torelli, G. Nap. 

Ed. 35 (1896) 238-. 
Measurement of cylinder. Rasch, J. W. N. 

Arch. Wisk. 7 (*1881) 117-. 
Mortality tables, theory. Samot, D.J. A. N. 

Arch. Wisk. 3 (M877) 145- . 
Numerical solution and reversion of series, 

remark on Woolhouse's paper. De Morgan, 

A. I. Act. J. 15 (*1870) 327-. 
Partial differences. Euler, L. [1777] St 

Pet. Ac. Sc. N. Acta 15 (1806) 3-. 

summation. Helm, G. Z. Mth. Ps. 22 
(1877) 400-. 

Plurality of integrals in calculus of differences. 

Poisson, S. D. [1800] Par. EC. Pol. J. 4 

(1801-2) (11 cah.) 173-. 
Progression, arithmetical, successive differences 

of powers of terms. Lhuilier, S. Gergonne 

A. Mth. 2 (1811-12) 185-. 
Progressions, arithmetical, whose terms are 

only approximately known. Lucas, F. C. B. 

96 (1883) 1026-. 

with 2nd and 3rd differences. Jadanza, N. 
G. Mt. 6 (1868) 375-; 7 (1869) 17-. 

Quadrature, arithmetical. Danielsson Hill, 
C. J. Stockh. Ak. Hndl. (1854) 405-. 

, Gauss's formula, and Hermite's formula of 
interpolation. Mansion, P. C. E. 104 
(1887) 488-. 

, , remainder in. Mansion, P. Brux. 

Ac. Bll. 11 (1886) 293-. 

Quadratures and interpolation, report on 
present knowledge of actual application. 
Merrifteld, C. W. B. A. Bp. (1880) 321-. 

Eational approximation to non-rational homo- 
geneous function. Eesal, H. A. C. E. 80 
(1875) 1185-. 

fractions, integration by finite differences of. 
Beyer, E. I. von. (xn) Bee. Mth. (Moscou) 
4 (1869-70) (Pt. 1) 297-; 5 (1870) (Pt. 1) 
64-, 145-. 

Beduction of higher differences when the 

constant increment is changed. Gudermann, 

C. As. Nr. 26 (1848) 315-. 
Beversion of series and its application to 

solution of numerical equations. Hagen, 

J. G. Am. Ph. S. P. 21 (1884) 93-. 
Second differences in interpolation, easy method 

of taking into account. Nell, . Arch. 

Mth. Ps. 70 (1884) 302-. 
Series of numbers and their interpolation. 

Ruff, H. Arch. Mth. Ps. 17 (1900) 426-. 
, summation by differences. Fuss, N. St 

Pet. Ac. Sc. Mm. 11 (1830) 246-. 
Simpson's formula and another. Catalan, 

E. C. N. A. Mth. 10 (1851) 412-. 
for approximation to areas. Daug, H. T. 

Stockh. Ofv. 17 (1860) 429-. 

method of interpolation, simplification. 
Parmentier, T. N. A. Mth. 15 (1876) 241-. 

rule, history. Heinrich, G. Bb. Mth. 1 
(1900) 90-. 

Solution of linear equations with large number 
of unknowns by successive approximation, 
Seidel's process. Mehmke, R. Eec. Mth. 
(Moscou) 16 (1893) 342-. 



Linear Substitutions 2000 

Solution of system of linear equations by succes- 
sive approximation. Mehmke, R. , & Nekrasov, 
P. A. [1892] Eec. Mth. (Moscou) 16 (1893) 
437-. 

Stirling's formula. Serret, J. A. C. E. 50 
(1860) 662-. 

. Bonnet, 0. C. E. 50 (1860) 862-. 

, elementary proof. Cesdro, E. N. A. 

Mth. 2 (1883) 43-. 

, extension. Hermite, C. Mth. A. 41 

(1893) 581-. 

and other interpolation formulae. Stuart, 

G. H. Mess. Mth. 19 (1890) 19-. 

series generalised, applications. Raabe, 
J. L. Zur. Mt. 3 (1853-55) 332-. 

for interpolation by symmetric differences. 

Merrifield, C. W. [1866] Mess. Mth. 4 

(1868) 110-. 
Successive differences of observations. Breger, 

. C. B. 93 (1881) 1119-. 
Sums and differences, theory, higher examples. 

Vdllas, A. Mag. Ak. Ets. (1850) 381-. 

,. (Schlomilch.) Oettinger, L. 
Grunert Arch. 13 (1849) 36-. 

Table of A TO O n -7-n(m). Cayley, A. [1879] 

Camb. Ph. S. T. 13 (1883) 1-. 
Time growth equation of trees. Blonay, H. de. 

Laus. S. Vd. Bll. 28 (1892) 207-. 

of vegetation in forests, interpolation 
applied to. Regneault, E. E. Nancy Mm. 
S. Sc. (1838) 169-. 

observations, interpolation. Thiele, T. N. 
Leip. As. Gs. Vjschr. 22 (1887) 302-. 

Trigonometrical formulae of interpolation. 

Fouret, G. C. E. 99 (1884) 963-, 1011-, 

1044, 1062-, 1140-. 
Trigonometry, finite differences in. Cagnoli, 

A. Mod. Mm. S. It. 8 (1799) 2 14-. 
Value of A'HV'VM" 1 where m and n are very 

large. Tait, P. G. Edinb. Mth. S. P. 5 

(1887) 83-. 
Values of A'H), tables. Herschel, J. \attributed 

to Lacroix in (m)]. N. A. Mth. 13 (1854) 272-. 
Variations, finite, analytical. Lorgna, A. M. 

Verona S. It. Mm. 4 (1788) 156-. 



Linear Substitutions. 
2000 General. 

Distributive operations and homography. Pin- 
cherle, S. Mil. I. Lomb. Ed. 29 (1896) 397-. 

Extraction of roots by substitutions. Levanen, 
S. Helsingf. Ofv. 34 (1892) 28-; Fschr. 
Mth. (1892) 135. 

Formulas given by Eisenstein and Hesse, note 
on two. Cayley, A. Crelle J. 29 (1845) 
54-. 

Integral functions of a system of mn variables 
which form m rows and n columns. Mertens, 
F. Krk. Ak. (Mt.-Prz.) Pam. 17 (1890) 
143- ; Fschr. Mth. (1890) 186-. 

Linear substitutions. Stephanos, C. Liouv. J. 
Mth. 6 (1900) 73-. 



126 



2010 Determinants 

Linear substitutions applied to theory of groups. 

Laurent, H. N. A. Mth. 16 (1897) 149-. 
, reduction. Jordan, C. Par. EC. Pol. 

J. 29 ( = Cah. 48) (1880) 15 1-. 
transformations of quadratic form. Boole, 

G. Camb. Mth. J. 4 (1845) 167-. 
, general theory. Boole, G. Camb. Mth. 

J. 3 (1843) 1-, 106-. 
, points in theory. Philippot, I. H. Liege 

S. Sc. Mm. 20 (1898) No. 9, 14 pp. 
Eational reversible substitutions. Kraus, L. 

Prag Sb. (1882) 338-; (1883) (Mth.-Vortr.) 

187-. 
Representation of binary homographies by 

points of space, with application to spherical 

rotations. Stephanos, C. Mth. A. 22 (1883) 

299-. 
Salmon's "Higher Algebra." Bellavitis, G. 

Yen. Mm. I. 9 (1860) 237-. 
Space, division by linear transformation groups. 

Dyck, W. Leip. Mth. Ps. B. 35 (1883) 61-. 
Theorem on two contrary substitutions. Lip- 

schitz, E. 0. S. Am. J. Mth. 1 (1878) 336-. 
. Sylvester, J. J. Am. J. Mth. 

1 (1878) 341-. 
Umbral notation. Barley, (Rev.) E. B. A. 

Bp. (1887) 600-. 



2010 Determinants. 

Adjoint minors. Landsberg, G. Crelle J. Mth. 

109 (1892) 225-. 
Adjugate determinant. Huir, T. [1894] Edinb. 

B. S. P. 20 (1895) 323-. 
Algebraic determinant, a special. Weihrauch, 

K. Z. Mth. Ps. 36 (1891) 34-. 

determinants, reduction. Eussell, W. H. L. 
E. A. Bp. (1885) 910-. 

expressions unaltered by certain substitu- 
tions. Glaisher, J. W. L. [1880] Mess. 
Mth. 10 (1861) 60-. 

reversibility, new theorem. Andre, D. Par. 
S. Mth. Bll. 24 (1896) 136-. 

Alternant of even number of letters, Jacobi's 

form. Muir, T. [1900] Edinb. B. S. P. 23 

(1902) 133- . 
, multiplication by symmetric function. 

Muir, T. [1899] Edinb. B. S. P. 22 (1900) 

539-. 
Alternants. Muir, T. [1879] Edinb. B. S. P. 

10 (1880) 102-. 
. Starkov. A. N. Es. S. Nt. Mm. (Mth.) 

10 (1889) 143-. 

. Muth, P. Crelle J. Mth. 122 (1900) 89-. 
, a class of. Loria, G. Prag Sb. (1897) 

(Mth.-Nt.) No. 57, 13 pp. 
, constant multiples of the difference product 

of the variables. Anglin, . [1888] Edinb. 

B. S. P. 15 (1889) 468-. 

and elliptic functions, identities connected 
with. Muir, T. [1900] Edinb. B. S. T. 40 
(1905) 187-. 

, history. Muir, T. [1900] Edinb. B. S. P. 

23 (1902) 93-. 
, summation of certain series. Anglin, A. H. 

[1887] Edinb. E. S. P. 14 (1888) 194-. 



Determinants 2010 

Alternants, theorems connected with. Anglin, 

A. H. [1886-88] Edinb. E. S. P. 13 (1886) 
823- ; 15 (1889) 381-. 

of the 3rd order, a formula of reduction 
for. Johnson, W. W. Am. J. Mth. 7 (1885) 
347-. 

, geometrical representation. 
Johnson, W. W. QJ. Mth. 21 (1886) 2 17-. 

4th order, calculation of co-factors. 
Johnson, W. W. Am. J. Mth. 7 (1885) 380-. 

Alternating functions. Cauchy, A. L. [1812] 

Par. EC. Pol. J. 10 (1815) (17 e cah.) 29-. 
. Jacobi, C. G. J. Crelle J. 22 (1841) 

360-. 
and applications. Cauchy, A. L. C. E. 

10 (1840) 178- ; 13 (1841) 939-. 
, a class of. Muir, T. [1887] Edinb. B. 

S. T. 33 (1888) 309-. 

of n variables. Scott, E. F. [1881] 
Mess. Mth. 11 (1882) 98-. 

, reduction to alternants. Johnson, W. W. 

Am. J. Mth. 7 (1885) 345-. 
used in elimination. Cauchy, A. L. C. 

B. 12 (1841) 414-. 

sums. Cauchy, A. L. C. B. 13 (1841) 939-. 
Arithmetical determinant, value of certain. 

Smith, H. J. S. L. Mth. S. P. 7 (1875-76) 
208-. 

determinants, certain. Cesdro, E. G. Mt. 
23 (1885) 182-, 367 ; Em. B. Ac. Line. Ed. 
1 (1885) 709-, 711-. 

of higher dimension. Gegenbauer, L. 

Wien Ak. Sb. 101 (1892) (Ab. 2 a) 425-. 

Bernoullian number expressed as a combina- 
tional determinant. Dupuis, N. F. Cn. B. 
S. P. & T. 7 (1890) (Sect. 3) 20-. 

Bernoulli's and Euler's numbers, representa- 
tion by determinants. Sachse, A. Arch. 
Mth. Ps. 68 (1882) 427-. 

Bibliography. Muir, T. QJ. Mth. 18 (1882) 
110- ; 21 (1886) 299-. 

Binary determinants. Brioschi, F. Crelle J. 
52 (1856) 133-. 

Bipartite functions. Muir, T. Edinb. E. S. 
T. 32 (1887) 461-. 

and determinants, new relations between. 

Muir, T. L. Mth. S. P. 16 (1884-85) 276-. 

Bordered determinants. Le Paige, C. M. M. 
H. H. Par. S. Mth. Bll. 8 (1880) 128-. 

. Arnaldi, M. G. Mt. 34 (1896) 209-. 

skew determinant. Muir, T. Edinb. E. S. 
P. 21 (1897) 342-. 

symmetric determinant, Cayley's theorem. 

Muir, T. QJ. Mth. 18 (1882) 46-. 
Cauchy 's determinant and aleph functions. 

Crocchi, L. [1878] G. Mt. 17 (1879) 2 18-, 

380. 
Circle touching three circles on a sphere. 

Trzaska, W. Par. T. Nauk. Sc. Pam. 1 

(*1871) 123- ; Bll. Sc. Mth. As. 6 (*1874) 

153. 
Circulant determinants. Torelli, G. Nap. Ed. 

21 (1882) 83-. 
Circulants. Studnicka, F. J. Mh. Mth. Ps. 

10 (1899) 193-. 
, detached theorems on. Muir, T. Edinb. 

E. S. T. 32 (1887) 639-. 



127 



2010 Determinants 

Circulants, final expansion. Muir, T. Mess. 
Mth. 14 (1885) 169-. 

of odd order. Muir, T. QJ. Mth. 18 (1882) 
261-. 

, resolution. Muir, T. Edinb. E. S. P. 21 

(1897) 369-. 
Co-axial minors of determinant of the fourth 

order. Muir, T. Edinb. B. S. T. 39 (1900) 

323-. 
, relations between. Nanson, E. J. 

Ph. Mg. 44 (1897) 362-. 
, expressibility of determinant in terms of 

its. Muir, T. Ph. Mg. 38 (1894) 537-. 
Combination of determinants, theorem. Syl- 
vester, J. J. Camb. and Dubl. Mth. J. 8 

(1853) 60-. 
Combinations applied to theory of determinants. 

Picquet, H. Par. EC. Pol. J. 28 (= Cah. 45) 

(1878) 201-. 
Combinatory analysis of determinants. Deruyts, 

J. Liege S. Sc. Mm. 11 (1885) No. 13, 11 pp. 

determinants. Zmurko, L. [1866] Wien D. 
27 (1867) (2 te Ab.) 63-. 

Commutants, property. Cayley, A. Ph. Mg. 

30 (1865) 411-. 
Composite determinants. Sylvester, J. J. Crelle 

J. Mth. 88(1880)49-. 
, Sylvester's memoir, remark. Borchardt, 

C. W. Crelle J. Mth. 89 (1880) 82-. 
Composition of determinants and bilinear forms, 

a mode of. Stephanos, C. G. Mt. 36 (1898) 

376-. 

systems of n 2 magnitudes with them- 
selves. Kronecker, L. Berl. Ak. Sb. (1890) 
1081-. 

Compound determinants. Scott, E. F. [1881] 

Mess. Mth. 11 (1882) 96-. 
. Van Velzer, C. A. (xn) [1881] J. H. 

Un. Cir. [1] (1882) 132. 
. Scott, E. F. [1882] L. Mth. S. P. 14 

(1882-83) 91-. 
. Van Velzer, C. A. Am. J. Mth. 6 

(1884) 164-. 
. Metzler, W. H. Am. J. Mth. 16 (1894) 

131- ; 20(1898)253-. 
, theorems on a special kind. Hunyady, 

J. (xn) Mag. Tud. Ak. Etk. (Mth.) 7 (1881) 

(No. 21) 15 pp. 
Concomitant determinants, certain. Eussell, 

J. W. L. Mth. S. P. 28 (1897) 430-. 
Constituents, elements, and minors of deter- 
minant, number of. Cunningham, A. J. 

Sc. 4 (1874) 212-. 
Continuant, condensation of. Muir, T. Edinb. 

Mth. S. P. 2 (1884) 16-. 
, development. Mollame, V. Kv. Mt. 3 

(1893) 47-. 
, the discriminant of a special quadratic 

form. Cesdro, E. Mathesis 12 (1892) 5-. 
Continuants. Muir, T. [1874] Edinb. E. S. 

P. 8 (1875) 229-, 380-. 
, note. Sylvester, J. J. Mess. Mth. 8 (1879) 

187. 
, properties. Studnicka, F. J. Prag Sb. 

(1886) (Mth.-Nt.) 3-. 
, roots of certain. Segar, H. W. Mess. 

Mth. 22 (1893) 171-. 



Determinants 2010 

Continuants, theorem. Muir, T. Ph. Mj. 3 

(1877) 137-, 360- . 
Convergence of infinite determinants. Koch, 

H. von [1896] Stockh. Ak. Hndl. Bh. 22 

(Afd. 1) (1897) No. 4, 31 pp. 
Coordinates, curvilinear. Combescure, E. Par. 

EC. Norm. A. 4 (1867) 93-. 
Cramer's determinants. Cantor, M. N. A. 

Mbh. 14 (1855) 113-. 

, or algebraic resultants. Le Cointe, 
J. L. A. (vra) A. Mt. 4 (1861) 233-. 

Cubic determinants. Armenante, A. [1866] G. 

Mt. 6 (1868) 175-. 

. Padova, E. G. Mt. 6 (1368) 182-. 

, forms of. Scott, E. F. [1881] L. Mth. 

S. P. 13 (1881-82) 33-. 
of infinite order. Cazzaniga, T. Mth. 

A. 53 (1900) 272-. 

and others of higher class, and deter- 
minants of alternate numbers. Scott, E. 
F. [1879] L. Mth. S. P. 11 (1879-80) 
!7-- 

, theory. Sziits, M. Mth. Termt. Ets. 

8 (1890) 220- ; Mth. Nt. B. Ung. 8 (1891) 

199-. 
Decomposition of systems of n 2 magnitudes, 

and application to invariants. Kronecker, L. 

Berl. Ak. Sb. (1889) 479-, 603-. 
Deduction of certain determinants from others. 

Segar, H. W. Mess. Mth. 22 (1893) 

57-. 
Determinant, a. Stern, M. A. Crelle J. 73 

(1871) 374-. 
, . Glaisher, J. W. L. As. Fr. C. E. 6 

(1877) 177-. 
, . Minozzi, A. G. Mt. 16 (1878) 148-. 

analysis. Cauchy, A. L. C. R. 42 (1856) 
366-. 

of any degree, development. Cadenat, A. 
As. Fr. C. E. (1900) (Pt. 2) 241-. 

, application of a. Zehfuss, G. Schlomilch 

Z. 7 (1862) 439-. 
, . Cherriman, J. B. (xn) [1882] 

Cn. B. S. P. & T. 1 (1883) (Sect. 3) 

, . Legoux, A. QJ. Mth. 19 (1883) 

41-. 

with binomial elements, development. Al- 
beggiani, M. G. Mt. 10 (1872) 279-. 

, calculation of a. Lemonnier, H. N. A. 

Mth. 18 (1879) 518-. 
, a certain. Zehfuss, G. Schlomilch Z. 3 

(1858) 298-. 
, . Gegenbauer, L. Wien Ak. Sb. 96 

(1888) (Ab. 2) 489-. 
, . Laisant, C. A. Par. S. Mth. Bll. 

17 (1889) 104-. 
, . Bourlet, G. N. A. Mth. 16 (1897) 

369-. 
, , theorem on. Mansion, P. Brux. Ac. 

Bll. 46 (1878) 892-. 
, development of a. Brioschi, F. [1857] 

Tortolini A. 1 (1858) 9-. 
, . Humbert, E. N. A. Mth. 4 

(1885) 289-. 
, particular. Caldarera, G. Catania 

Ac. Gioen. At. 7 (1894) Mm. 8, 15 pp. 



128 



2010 Determinants 

Determinant, evaluation of a certain. Cayley, 

A. QJ. Mth. 2 (1358) 163-. 
, . Dostor, G. Arch. Mth. Ps. 

64 (1879) 57-. 
, . Berry, A. Camb. Ph. S. P. 

10 (1900) 2-. 
, . Crawford, L. Edinb. Mth. 

S. P. 18 (1900) 25-. 

expressions for Laplace's coefficients, Ber- 
noulli's and Euler's numbers, etc. Glaisher, 
J. W. L. [1876-79] Mess. Mth. 6 (1877) 49-; 
7 (1378) 160- ; 8 (1879) 158-. 

the sum of a harmonical progression. 

Muir, T. [1877] Edinb. B. S. P. 9 (1878) 
361-. 

formed bv bordering product of two deter- 
minants. Muir, T. Mess. Mth. 11 (1882) 
161-. 

forms and their applications. Echols, W. H. 
A. Mth. 6 (1891-92) 135- ; 7 (1892-93) 11-, 
93-, 109-. 

of four points in plane, with respect to a 
5th. Laisant, C. A. Lisb. J. Sc. Mth. 5 
(1898) 205-. 

, geometrical and statical interpretation of a. 

Walton, W. QJ. Mth. 4 (1861) 252-. 
identities in study of perspective triangles. 

Caspary, F. [1881] Crelle J. Mth. 95 (1883) 

36-. 
, maximum value of a certain. Davis, E. W. 

(xn) [1882] J. H. Un. Cir. [2] (1883) 22. 

minors, certain aggregates of. Muir, T. 
[1900] Edinb. K. S. P. 23 (1902) 142-. 

, new development. Shaw, J. B. [1900] N. 
Y. Am. Mth. S. fill. 7 (1901) 244, 256-. 

notations and evaluation of a special deter- 
minant. Moore, E. H. A. Mth. 1 (1900) 
177-. 

occurring in calculation of symmetric 
functions. Gubler, E. Ziir. Vjschr. 35 
(1890) 79-. 

with polynomial elements, development. 
Albeggiani, M. [1874] G. MS. 13 (1875) 1-. 

, properties of. Wisselink, D. B. N. Arch. 

Wisk. 3 (* 1877) 84-. 
, property of a. Sardi, C. G. Mt. 2 (1864) 

of sines and cosines. Scott, E. F. Mess. 
Mth. 10 (1381) 142-. 

Smith and Mansion. Cesar -o, E. Par. 

EC. Norm. A. 2 (1885) 425-. 
, special form. Glaisher, J. W. L. [1878] 

QJ. Mth. 16 (1879) 15-. 

of system compounded of two others, repre- 
sentation. Hensel, K. Acta Mth. 14 (1890- 
91) 317-. 

of functions. Bertrand, J. Liouv. J. 

Mth. 16 (1851) 212-. 
, vanishing. Heawood, P. J. Mth. Gz. 1 

(1900) 344. 

with vanishing diagonal, Baltzer on number 
of terms. Monro, C. J. [1872] Mess. Mth. 
2 (1873) 38-. 

| a rs | , number of terms when a rr = 0. 
Hansted, B. G. Teix. J. Sc. 2 (1880) 154-. 

of 4th order, unique property of an axi- 
symmetric. Muir, T. A. Mth. 1 (1884- 
85) 31-. 



Determinants 2010 

Determinant of 6th order, peculiar. Muir, T. 
Ph. Mg. 31 (1391) 429-. 

, development of a special. 
Muir, T. Mess. Mth. 13 (1884) 95-. 

mnth order, development. Muir, T. 
Edinb. R. S. T. 39 (1900) 623-. 

Determinantal form of highest common factor. 
Scheibner, W. Leip. Mth. Ps. B. 40 (1888) 

Determinants. Jacobi, C. G. J. Crelle J. 22 

(1841) 285-. 
. Catalan, E. C. Brux. Ac. Bll. 13 (1846) 

534-. 
. Bazin, . Liouv. J. Mth. 18 (1851) 

145-. 

. Terquem, 0. N. A. Mth. 10 (1851) 124-. 
. Bazin, . Liouv. J. Mth. 19 (1854) 

209-. 
. Newman, F. W. B. S. P. 8 (1856-57) 

426-. 
. Oliver, J. E. Camb. (M.) Mth. M. 3 

(1860) 86-. 

. Battaglini, G. Nap. Ed. 1 (1862) 101-. 
. Tait, P. G. Mess. Mth. 1 (1862) 25-. 
. Homer, J. [1865] QJ. Mth. 8 (1867) 

. Battaglini, G. G. Mt. 9 (1871) 136-. 
. Baltzer, R. (ix) Leip. Mth. Ps. B. 25 

(1873) 523-. 
. Scott, R. F. Mess. Mth. 8 (1879) 182- ; 

12 (1883) 105-. 
. Lindelof, L. L. Helsingf. Ofv. 22 (1880) 

123-. 

. Young, T. E. I. Act. J. 26 (1887) 149-. 
. Gegenbauer, L. Wien Ak. Sb. 96 (1888) 

(Ab. 2) 5-; 97 (1889) (Ab. 2a) 154-. 
. Ponte Horta, F. da. [1890] Lisb. J. Sc. 

Mth. 2 (1892) 67-. 
. Campbell, J. E. [1892] L. M,h. S. P. 24 

(1893) 67-. 
. Schendel, L. Z. Mth. Ps. 38 (1893) 84-. 

of alternate numbers. Spottiswoode, W* 
L. Mth. S. P. 7 (1875-76) 100-. 

in analytical mechanics. Cohen, A. Phil. 
Trans. (1862) 469-. 

, application. Jamet, V. N. A. Mth. 1& 

(1877) 372-. 
, to contact of circles and spheres. Bauer > 

C. W. N. A. Mth. 19 (1860) 440-. 
, curves of 4th order, etc. Hesse, L. 0. 

[1853] Crelle J. 49 (1855) 243-. 
, moments. Durrande, H. N. A.. 

Mth. 12 (1873) 265-. 
, , note. Gerono, G. C. N. A. Mth. 9 1 

(1870) 392-. 
, applications. Rubini, R. Tortolini A. 8: 

(1857) 179-. 
, . Neuberg, J. J. B. (xn) Mathesis 3 

(1383) 29-. 
, to algebra and geometry. Versluys, J. 

Arch. Mth. Ps. 50 (1869) 157-, 210- ; 51 

(1870) 49-; 53 (1871) 137-. 
, geometry. Joachimstluil, F. Crelle 

J. 40 (1850) 21-. 
, . Mertens, F. (vm) [1873] Crelle 



J. 77 (1874) 102-. 

, 6 



metrical). Frobenius, G. [1874] 
Crelle J. Mth. 79 (1875) 185-. 



VOL. I. 



129 



2010 Determinants 

Determinants, applications to geometry of 
n dimensions. Rahusen, A. E. Delft 6c. 
Pol. A. 4 (1888) 104-. 

arising in cyclotomy. Hermes, J. Arch. 
Mth. Ps. 6 (1888) 276-. 

of binomial coefficients. Zeipel, E. V. von. 
Lund Acta Un. 2 (1865) (Mth.) No. 2, 68 pp. ; 
8 (1871) (Mth.) No. 3, 36 pp. 

. Gilnther, S. Z. Mth. Ps. 24 

(1879) 96-. 

. Studnitka, F. J. Prag Sb. (1879) 

292-. 
, Borchardt's theory. Lerch, M. Casopis 

23 (1894) 76-; Fschr. Mth. (1893-94) 213. 
, calculation. Jiirgens, E. D. Nf. Vh. (1900) 

(Th. 2, Htilfte 1) 7-. 
, certain. Eugenio, V. G. Mt. 8 (1870) 

285-. 
, . Glaisher, J. W. L. B. A. Bp. (1876) 

(Sect.) 13-. 

, . Voss, A. E. Mth. A. 13 (1878) 161-. 
, . Escherich, G. von. Mh. Mth. Ps. 3 

(1892) 68-. 

of certain class (Grevy's), theorems on. 
Bottcher, L. E. Krk. Ak. (Mt.-Prz.) Bz. 18 
(1901) 382-; Crc. Ac. Sc. Bll. (1900) 227-. 

, class. Zeipel, E. V. von. Stockh. Ofv. 

19 (1862) 439-. 
, . Dickson, J. D. H. [1878] Edinb. B. 

S. T. 28 (1879) 625-. 

, . Loria, G. G. Mt. 26 (1888) 329-. 
, condensation (a method of calculation). 

Dodgson, C. L. [1866] B. S. P. 15 (1867) 

150-. 

in conies. Pasch, M. Crelle J. Mth. 89 

(1880) 247-. 

connected with algebraical expressions 
having same form as component factors. 
Roberts, S. Mess. Mth. 8 (1879) 138-. 

and continued fractions, convergence. 
Koch, H. von. C. B. 120 (1895) 144-. 

of co-variants. Scott, R. F. Mess. Mth. 10 

(1881) 142-. 

derived from differential coefficients, new 
species. Studnicka, F. J. Mh. Mth. Ps. 10 
(1899) 338-. 

of determinants. Ovidio, E. d\ [1876-90] 
Tor. Ac. Sc. At. 11 (1875-76) 949-; 12 
(1876) 331- ; 26 (1891) 131-. 

, development, new method, and application 

to finding resultant of any two equations. 

Bonolis, A. [1882] G. Mt. 21 (1883) 

336-. 
, developments. Bonolis, A. [1876] G. 

Mt. 15 (1877) 113-. 
, . Capelli, A. Nap. Ed. 28 (1889) 58-. 

of differences. Raimondi, R. G. Mt. 26 
(1888) 185-. 

, divisors. Frobenius, G. Berl. Ak. Sb. 
(1894) 31-. 

and duadic disynthemes, note. Sylvester, 
J. J. Am. J. Mth. 2 (1879) 89-, 214-. 

, elementary divisors of, application to linear 
differential equations. Sauvage, L. Mars. 
Fac. Sc. A. 6 (1897) Fasc. 5, 9 pp. 

, treatment. Hesse, L. O. G. Mt. 10 
(1872) 217-, 325-. 



Determinants 2010 

Determinants whose elements are composed 
of elements of adjoint series, theorems. 
Hunyady, J. (xn) Mag. Tud. Ak. Etk. 
(Mth.) 1 (1881) (No. 19) 27 pp. 

--- rational fractions. Scott, R. F. 
Mess. Mth. 11 (1882) 165-. 

---- squares of lines joining vertices of 
two tetrahedrons. Siebeck, H. Crelle J. 62 
(1863) 151-. 

--- sums of powers. Studnicka, F. J. 
Prag Ceske Ak. Fr. Jos. Bz. (Tfida 2) 9 
(1900) Art. 4, 8 pp. ; Fschr. Mth. (1900) 
156. 

of even order. Brioschi, F. Crelle J. 52 
(1856) 133-. 

figurate numbers. Gaidar era, F. G. 
Mt. 9 (1871) 223-. 

-- form 



Zehfuss, G. Schlomilch Z. 4 (1859) 232-. 

formed of elements with any number of 
indices. Garbieri, G. [1876] G. Mt. 15 
(1877) 89-. 

from the same elements, relations 
between. Pascal, E. Mil. I. Lomb. Bd. 
29 (1896) 436-. 

?i 2 elements. Bagnera, G. 
G. Mt. 25 (1887) 228-. 

, formula in. Pincherle, S. Bologna Bd. 

(1883) 105-. 

, -- . Mertens, F. Wien Ak. Sb. 91 
(1885) (Ab. 2) 622-. 

, -- . Nielsen, N. N. Ts. Mth. 7 (B) 

1896) 59-; Fschr. Mth. (1896) 111. 

, -- . Schulze, E. Z. Mth. Ps. 42 (1897) 
313-. 

, -- . Valentiner, H. N. Ts. Mth. 9 (B) 

1898) 15-. 

, -- . Schulze, E. Z. Mth. Ps. 44 (1899) 
167-. 

, formula. Rubini, R. Nap. Bd. 5 (1866) 
109-. 

, . Starkov, A. P. Kazan S. Nt. (Ps.- 
Mth.) P. 3 (1885) 75-. 

and functions, fractional. Dietrich, M. 
Crelle J. 69 (1868) 190-. 

of functions and their differentials. Pasch, 
M. Crelle J. Mth. 80 (1875) 177-. 

, a general property of two. Kretkowski, W. 

xn) [1882] Krk. Ak. (Mt.-Prz.) Pam. 9 

(1884) 45-; Fschr. Mth. (1884) 122-. 

, generalisation of a theorem. Marcolongo, 
R. G. Mt. 25 (1887) 298-. 

, geometrical application. IVhite, H. S. 
A. Mth. 1 (1900) 103-. 

, interpretation. [Barrl de'] Saint-Venant, 
. C. B. 36 (1853) 582-. 

, significance of certain. Bauer, G. 
Munch. Sb. (1872) 345-. 

, treatment. Waelsch, E. Mh. Mth. Ps. 
9 (1898) 207-. 

of higher dimensions. Gegenbauer, L. 
[1880-90] Wien Ak. D. 43 (1882) (Ab. 2) 
17- ; 46 (1883) (Ab. 2) 291- ; 49 (1885) 
(Ab. 2) 225-; 50 (1885) (Ab. 1) 145- ; 57 

1890) 735-. 



130 



2010 Determinants 

Determinants of higher dimensions and applica- 
tion to formation of invariants. Escherich, 
G. von. [1880] Wien Ak. D. 43 (1882) 
(Ab. 2) 1-. 

, history and theory. Giinther, , D. Nf. 
Tbl. (*1874) 78-. 

, identical relation between certain. Pain- 
leve, P. Par. S. Mth. Bll. 22 (1894) 116-. 

involving powers of circles. Johnson, W. W. 
J. H. Un. Cir. [10 (1890-91)] 46. 

whose leading elements are in A.P. 
Cazzaniga, T. Mil. I. Lomb. Ed. 29 (1896) 
541- 

with magic matrix. Caldarera, F. Palermo 
G. Sc. Nt. 1 (1866) 173-. 

of a matrix, relations between. Valilen, 
K. T. Crelle J. Mth. 112 (1893) 306-. 

, . Ahrens, W. Z. Mth. Ps. 

42 (1897) 65-. 
maximum value. Scarpis, U. Mil. I. 

Lomb. Ed. 31 (1898) 1441-. 
, method of solving. Macloskie, G. A. Mth. 

1 (1900) 74-. 

of minor determinants. Franke, E. [1862] 
Crelle J. 61 (1863) 350-. 

and minors of original and adjoint systems. 
Studnicka, F. J. Casopis 1 (* 1872) 6-; 
Fschr. Mth. (1872) 59. 

modern algebra in lower mathematics. 
Prange, A. J. A. N. Arch. Wisk. 17 (1890) 
158- ; Fschr. Mth. (1890) 181-. 

, multiplication. Gomes Teixeira, F. G. 

Teix. J. Sc. 3 (1881) 185-. 
, . Loria, G. G. Teix. J. Sc. 7 (1886) 

101-. 
, . Cazzaniga, T. A. Mt. 2 (1899) 

229-. 
, , application. Souillart, C. N. A. Mth. 

19 (1860) 320-. 
, and multiplication of complex quantities. 

Palmstrftm, A. Arch. Mth. Ntvd. 13 (1890) 

128- ; Fschr. Mth. (1890) 409. 
, multiplication, elementary proof of 

theorem. Falk, M. B. A. Ep. (1878) 

473-. 
, formula, verification. Weyr, E. Prag 

Sb. (1880) 55-. 
, of minors. Zancevskij, I. M. [1894] 

Eec. Mth. (Moscou) 17 (1395) 587-; Fschr. 

Mth. (1893-94) 217. 

; (n - l)th power of a symmetric deter- 
minant by 2nd power of another. Muir, T. 

Am. J. Mth. 4 (1881) 273-. 
, rule. Le Paige, C. M. M. H. H. Par. 

S. Mth. Bll. 9 (1381) 67-. 
, , geometric application. Mertens, F. 

Prag Sb. (1880) 207-. 
, theorem, proof. Kdnig, J. Mth. A. 14 

(1879) 507-. 
, , . Falk, M. Gott. Nr. (1885) 

181-. 
, of two of nih degree. Hoza, F. 

Arch. Mth. Ps. 59 (1376) 403-. 
, of two of same degree. Presle, A. de. 

Par. S. Mth. Bll. 14 (1886) 157-. 

of n dimensions. Tanner, H. W. L. L f 
Mth. S. P. 10 (1878-79) 167-. 



Determinants 2010 

Determinants, new formula, with reference 
to theory of linear differential equations. 
Anissimoff, W. Mth. A. 51 (1899) 388-. 

, numerical calculation of class, and con- 
tinued fractions. Dickson, J. D. H. L. 
Mth. S. P. 10 (1878-79) 226-. 

of p dimensions, theory. Zajqczkowski, W. 
(xn) [1880] Krk. Ak. (Mt.-Prz.) Pam. 6 
(1881) (1 ter)-. 

with polynomial elements. Muir, T. Mess. 
Mth. 13 (1884) 135-. 

of powers. Mitchell, 0. H. Am. J. Mth. 4 
(1381) 341-. 

, powers of. Weltzien, C. Mth. A. 50 

(1898) 282-. 
, product of two. Hunyady, E. von. Z. 

Mth. Ps. 11 (1366) 359-. 
, . Weltzien, C. Mth. A. 42 (1893) 

598-. 
, proof of formula due to Cauchy. Echols, 

W. H. A. Mth. 8 (1893-94) 21-. 
, geometric theorem by. Mansion, P. 

[1875] Mess. Mth. 5 (1876) 158-. 
, properties. Dostor, G. (vn) Arch. Mth. 

Ps. 56 (1374) 238-. 
, property of certain. Burnside, W. Mess. 

Mth. 23 (1894) 112-. 
, deduced from substitution theory. 

Scarpis, U. G. Mt. 37 (1899) 73-. 
, , new. Studnicka, F. J. Prag Sb. 

(1380) 50-. 
, a proposition in theory of. Drude, P. 

Gott. Nr. (1887) 118-. 
, . Baltzer, E. Gott. Nr. 

(1887) 389-. 
, . Voss, A. Munch. Ak. Sb. 

19 (1390) 329-. 

of quadratic forms. Brioschi, F. N. A. 
Mth. 11 (1852) 307-. 

, rational proof of first principles. Laquiere, 
E. M. As. Fr. C. E. (1381) 226-. 

of a rectangular matrix. Pascal, E. A. 
Mt. 24 (1896) 241-. 

, relation between two. Del Ee, A. G. Mt. 

19 (1881) 116-. 
, relations between certain. Deruyts, J. 

Brux. Ac. Bll. 23 (1392) 507-. 

of several functions of one variable. 
Frobenius, G. (vn) [1873] Crelle J. 77 
(1874) 245-. 

sines and cosines, method of evaluation. 

Scott, R. F. Mess. Mth. 8 (1379) 155-. 
Smith. Mansion, P. (xn) Brux. S. 

Sc. A. 2 (1878) (Pt. 2) 211- . 
, solution of question relating to. Hadamard, 

J. Bll. Sc. Mth. 17 (1893) 240-. 
, some forms. Lerch, M. Prag Ceske Ak. 

Fr. Jos. Ez. (Tflda 2) 8 (1899) Art. 12, 

16 pp. ; Fschr. Mth. (1899) 151-. 
, hitherto unproved theorems. Muir, T. 

Edinb. E. S. P. 18 (1892) 73-. 
, whose terms are distances of point from 

3 points. Cayley, A. QJ. Mth. 5 (1862) 
381-. 

, squared distances of points. 

Cayley, A. QJ. Mth. 3 (1860) 275-. 
, theorem. Mirza-Nizam, . N. A. Mth. 

4 (1865) 500-. 



131 



i2 



2010 Determinants 

Determinants, theorem. Stern, M. A. [1865] 

Crelle J. 66 (1866) 285-. 
, . Hesse, L. 0. Crelle J. 69 (1868) 319-. 
_, _. Sardi, C. G. Mt. 6 (1868) 357-. 
, . Gundelfinger, S. Z. Mth. Ps. 18 

1873) 312-. 

_, __. Cayley, A. QJ. Mth. 15 (1878) 55-. 
, . Glaisher, J. W. L. Mess. Mth. 8 

(1879) 140-. 

, . Fact de Bruno, F. Am. J. Mth. 3 

(1880) 154-. 

__, _. Daublebsky von Sterneck, R. Mh. 

Mth. Ps. 6 (1895) 205-. 
, . Metzler, W. H. Am. J. Mth. 20 

(1898) 273-. 
, . Lovett, E. O. A. Mth. 12 (1898-99) 

161-. 

, . Kantor, S. Gott. Nr. (1899) 272-. 
, and applications. Siacci, F. Tor. At. 

Ac. Sc. 7 (1871-72) 772-. 
, its converse. Puchta, A. [1877] 

Wien Ak. D. 38 (1878) (Ab. 2) 215-. 
, , fundamental. Sylvester, J. J. Ph. 

Mg. 2 (1851) 142-. 
, , . Becker, J. C. Z. Mth. Ps. 16 

1871) 526-. 
, of Glaisher's. Scott, R. F. QJ. Mth. 

17 (1881) 129-. 
_, Jacobi's. Segar, H. W. Mess. Mth. 

21 (1892) 148-. 
, Netto relating to. Pascal, E. Em. 

E. Ac. Line. Bd. 5 ^1896) (Son. 1) 188-. 
, , new. Studnicka, F. J. Prag Sb. (1873) 

342-; Casopis 9 (*1880) 97-; Fschr. Mth. 

(1880) 114. 
, , . Puchta, A. [1881] Wien Ak. D. 

44 (1882) (Ab. 2) 277-. 
, of Sylvester's, proof. Igel, B. Mh. 

Mth. Ps. 9 (1898) 47-. 
, theorems. Cauchy, A. L. C. E. SI (1845) 

407-. 

, . Mogni, A. G. Mt. 3 (1865) 10-. 
, . Giinther, S. Erlang. Sb. Ps. Md. S. 

5 (1873) 88-. 
, . Scott, R. F. [1878] Mess. Mth. 8 

(1879) 33-. 
, . Studnicka, F. J. Prag Sb. (1896) 

(Mth.-Nt.) No. 6, 5 pp. 
, and application to proofs of Pascal's and 

Brianchon's theorems. Mertens, F. Crelle 

J. Mth. 84 (1878) 355-. 
, , certain. Nanson, . Crelle J. Mth. 

122 (1900) '179-. 
, , elementary. Spottiswoode, W. [1853] 

Crelle J. 51 (1856) 209-, 328-. 
, , . Ferrers, N. M. QJ. Mth. 1 (1857) 

364. 
, , general. Muir, T. [1879] Edinb. E. 

S. T. 29 (1880) 47-. 
, , homoloidal law, theory of orders, etc. 

Sylvester, J. J. Ph. Mg. 37 (1850) 363-. 
, of Mainardi. Bellavitis, G. Ven. At. 

(1857-58) 623-; (1858-59) 334-. 
, , new. Studnicka, F. J. Casopis 1 

(*1872) 203-. 
, , proofs. Janni, V. G. Mt. 12 (1874) 



Determinants 2010 

Determinants, theorems, two. Zehfuss, G. 

Schlomilch Z. 7 (1862) 436-. 
, _, _. Ovidio, E. d\ G. Mt. 1 (1863) 

135-. 
, , . Kapteyn, W. N. Arch. Wisk. 10 

(1884) 180-. 
, , . Netto, E. Acta Mth. 17 (1893) 

199-. 
, theory. Cayley, A. [1843] Camb. Ph. S. 

T. 8 (1849) 50-. 
, . Bellavitis, G. Ven. Mm. I. 7 (1857) 

67-. 
_, _. Cayley, A. Ph. Mg. 21 (1861) 

180-. 
, . Dietrich, M. Arch. Mth. Ps. 44 (1865) 

344-. 
, . Kronecker, L. [1869] Crelle J. 72 

1870) 152-. 
__, __. Veltmann, W. Z. Mth. Ps. 16 (1871) 

5 16-. 
_, _. Wey ranch, J. J. [1871] Crelle J. 74 

(1872) 273-. 
, . Studnicka, F. J. Prag Sb. (1872) 

78-; Casopis 2 (*1873) 282-; Fschr. Mth. 

(1873) 90. 
_, _. Weihrauch, K. Z. Mth. Ps. 19 (1874) 

354-. 
, . Studnicka, F. J. Prag Sb. (1877) 

120-. 
, . Fiirstenau, E. [1879] Crelle J. Mth. 

89 (1880) 86-. 
, . Igel, B. [1880] Wien Ak. Sb. 82 

(1881) (Ab. 2) 1288-. 
, . Landre, C. L. N. Arch. Wisk. 6 

(1880) 208-. 
, . Rados, G. Mth. Termt. Ets. 4 

(1886) 268-; Mth. Nt. B. Ung. 8 (1891) 

60-. 
, . SzOts, N. von. Mth. A. 33 (1889) 

477-. 

, . Igel, B. Mh. Mth. Ps. 3 (1892) 55-. 
, . Miller, E. [1892] Kan. Un. Q. 1 

(1893) 133-. 
, . StudniSka, F. J. Casopis 25 (1896) 

241- ; Fschr. Mth. (1896) 108; Mh. Mth. 

Ps. 10 (1899) 1-. 
, , analytical. Schering, E. Gott. Ab. 

22 (1877) (Mth.) 41 pp. ; C. E. 86 (1878) 

1387-. 
, , application of modular systems to. 

Netto, E. Crelle J. Mth. 108 (1891) 144-. 
, based on solution of groups of general 

linear equations. Matzka, W. [1877] Prag 

Ab. 9 (1878) (Mth.) (No. 1) 61 pp. 



^, (chess problem). Serdobinskil, V. E. 
(xn) [1877] Eec. " 
83) (Pt. 1) 74-. 



Mth. (Moscou) 10 (1882- 



, , elementary. Gomes Teixeira, F. G. 
Teix. J. Sc. 1 (1878) 138-. 

, , elements. Hoppe, R. Arch. Mth. Ps. 
65 (1880) 65-. 

, , in the historical order of its develop- 
ment. Muir, T. [1886-89] Edinb. E. S. P. 
13 (1886) 547-; 14 (1888) 452-; 15 (1889) 
481- ; 16 (1890) 207-, 389-, 748-. 

, , method of stating. Kneser, A. Dorpat 
Sb. 9 (1892) 522-. 



132 



2010 Determinants 

Determinants, theory, origin and develop- 
ment. Studnicka, F. J. Casopis 5 (* 1876) 
1-, 88-, 193-, 279-. 

t ) third fundamental proposition, new 
method of deduction. Studnicka, F. J. 
Casopis 17 (1888) 193- ; Fschr. Mth. (1888) 
143. 

of 3rd order, note. Tait, P. G. [1866] 
Edinb. B. S. P. 6 (1869) 59-. 

4th order, development. Guimaraes, R. 

As. Fr. C. K. (1897) (Pt. 2) 129-. 

3 ; 4 and 5 rows, rules for their calcula- 
tion by inspection. Teixeira, J. P. G. 
Teix. J. Sc. 11 (1892) 88-; Fschr. Mth. 
(1392) 141. 

with triple indices, product expressed as one 
ordinary determinant. Gassparis, A. de. Rm. 
R. Ac. Line. T. 3 (1379) 44-. 

and m indices, theorems. Gasparis, 

A. de. Nap. Rd. 7 (1368) 118-. 
vector constituents. Chapman, C. H. 

J. H. Un. Cir. [9 (1889-90)] 77. 
Determination of four functions to satisfy a 

certain equation. Vivanti, G. Palermo Cir. 

Mt. Rd. 6 (1892) 100-. 
Dialytic determinant, evaluation of a certain. 

Taylor, W. W. [1895] L. Mfch. S. P. 27 

(1396) 60-. 

Discriminating symmetrical determinant. Syl- 
vester, J. J. Crelle J. Mth. 88 (1380) 6-. 
Distances between points, equation connecting 

mutual. Muir, T. Edinb. Mth. S. P. 3 

(1885) 34-. 
, relations. Brioschi, F. N. A. Mth. 

14 (1855) 172-. 
Double series, two, arising from number of 

terms in determinants. Dickson, J. D. H. 

L. Mth. S. P. 10 (1878-79) 120- . 
Doubly orthosymmetrical determinants. Weih- 

rauch, K. Z. Mth. Ps. 26 (1381) 64-, 

132-. 

skew determinants. Sylvester, J. J. C. R. 
89 (1879) 24-. 

Equation for max. and min. of ?i-ary quadric. 
Gravelaar, N. L. W. A. N. Arch. Wisk. 4 
(*1878) 113-. 

Equations, symmetrical linear, with indeter- 
minate coefficients, solution by determinants. 
Stockwell, J. N. Gould As. J. 6 (1361) 
145-. 

Factorisation of characteristic equation of in- 
duced substitutions. Rados, (?. Mth. Termt. 
Ets. 17 (1899) 66-; Mth. Nt. B. Ung. 17 
(1901) 248-. 

Factors of a special form of determinant. 
Glaisher, J. W. L. QJ. Mth. 15 (1878) 
347-. 

Formula of Lagrange generalised by Cauchy. 
Barbier, E. C. R. 96 (1383) 1345-. 

Liouville's. Lucas, F. C. R. 70 (1370) 

1167-. 

Lucas, connecting n quantities and their 

sum, proof. Albeggiani, M. G. Mt. 13 
(1875) 107-. 

Formulas, fundamental, of spherical trigono- 
metry derived from theorem in determinants. 
Studnicka, F. J. Prag Sb. (1375) 1-. 



Determinants 2010 

Formulae relative to polar operations. Capelli, 

A. G. Mt. 32 (1894) 376-. 
Functional determinant, property. Brioschi, F. 

QJ. Mth. 1 (1857) 365-. 

determinants. Jacobi, C. G. J. Crelle J. 
22 (1341) 319-. 

. Combescure, E. Par. EC. Norm. A. 4 

(1367) 93-. 
. Casorati, F. [1874] Mil. I. Lomb. 

Mm. 13 (1377) 181 -. 
. Faa de Bruno, F. Mth. A. 18 (1881) 

280-. 
. Kraus, L. Wien Ak. Sb. 90 (1885) 

(Ab. 2) 813-. 
_ __. Torelli, G. Palermo Cir. Mt. Rd. 

7 (1893) 75-. 
, application. Trzaska, W. Par. T. 

Nauk Sc. Pam. 1 (*1871) 113- ; Bll. Sc. Mth. 

As. 6 (*1874) 153. 
, elementary proof of theorem. Nanson, 

E. J. [1877] Mess. Mth. 7 (1878) 120-. 
and Jacobian matrices. Giordano, G. 

G. Mt. 38 (1900) 210-. 
, property. Clebsch, R. F. A. Crelle 

J. 69 (1868) 355-; 70 (1869) 175-. 
, and application to implicit functions. 

Gilbert, P. [1869] Brux. Ac. Sc. Mm. 38 

(1871) 12 pp. 
, rational. Mansion, P. [1879] Mess. 

Mth. 9 (1880) 30-. 
, , generalisation. Mertens, F. Krk. 

Ak. (Mt.-Prz.) Pam. 16 (1889) 60-; Fschr. 

Mth. (1889) 151-. 
, _, theorems. Anglin, A. H. [1886] 

Ir. Ac. P. 4 (1884-88) 645-. 
, theorem (Hesse). Zmurko, W. Par. 

T. Nauk Sc. Pam. 1 (*1871) 89-. 
, (Jacobi). Donkin, W. F. Camb. 

and Dubl. Mth. J. 9 (1854) 161-. 

t theory. Neumann, C. Mth. A. 1 
(1869) 208-. 

Functions analogous to determinants. Dah- 

lander, G. R. Stockh. Ofv. 20 (1863) 295-. 
Fundamental operations of arithmetic, genera- 
lisation. Schapira, H. D. Nf. Tbl. (*1882) 

128-. 
Geometrical series of 2nd order. Hochheim, A. 

Magdeb. Nt. Vr. Jbr. u. Ab. (1886) 127- ; 

(1887) 25-. 
Goniometrical determinants, some. Weihrauch, 

K. Z. Mth. Ps. 36 (1891) 71-. 
Grassmann's method applied to prove theorems 

in determinants. Miiller, E. Z. Mth. Ps. 

44 (1899) 28-. 
Harmonic determinant, condition for equal 

roots. Tarleton, F. A. [1887] Ir. Ac. P. 1 

(1889-91) 10-. 
Hesse, theorem (Hessian determinant). Gor- 

dan, P. Erlang. Ps. Md. S. Sb. 8 (1876) 89-. 
Hessian. Segre, C. Rm. R. Ac. Line. Rd. 

4 (1895) (Sem. 2) 143-. 
, application of exponential polygon. Eddy, 

H. T. Des Moines Anal. 2 (1875) 104-. 
, change of independent variables in a. 

Nanson, F. J. Mess. Mth. 25 (1896) 139-. 

determinant. Voss, A. Mth. A. 30 (1887) 
418-. 



133 



2010 Determinants 

Hessian determinant of Hessian of surface of 
3rd order. Bauer, G. Munch. Ak. Ab. 14 
(1883) (Ab. 3) 77-. 

determinants, theory. Pasch, M. Crelle 
J. Mth. 80 (1875) 169-. 

Higher algebra, and theorems in determinants. 
Zeipel, E. V. von. Stockh. Ak. Hndl. 3 
(1859-60) 32 pp. 

Identities, composition, and relation to deter- 
minants. RensJuiio, A. Mess. Mth. 4 
(1868) 34-. 

in determinants. Hunyady, J. [1882] (xn) 
Mag. Tud. Ak. Etk. (Mth.) 9, No. 10 (1882) 
19 pp. ; (x) Crelle J. Mth. 94 (1883) 171- 

rational functional determinants. 
Prouhet, E. N. A. Mth. 15 (1856) 86-. 

Infinite determinants. Poincare, H. Par. S. 

Mth. fill. 14 (1886) 77-. 
. Roberts, E. H. A. Mt. 10 (1895-96) 

35-. 

. Cazzaniga, T. A. Mt. 26 (1897) 143-. 

applied to functional equations. Koch, 

H. von. Stockh. Ak. Hndl. Bh. 25 (1900) 

(Afd. 1) No. 5, 24 pp. 

linear homogeneous differential 

equations. Koch, H. von. Stockh. Ofv. 

(1890) 225-, 499-; Fschr. Mth. (1890) 316. 

, convergence. Koch, H. von. [1896] 
Stockh. Ak. Hndl. Bh. 22 (Afd. 1) (1897) 
No. 4, 31 pp. 

, theory. Koch, H. von. Stockh. Ofv. 

(1890) 411- ; Fschr. Mth. (1890) 185. 
Integral elements, reduction of systems of n a . 

Kronecker, L. Crelle J. Mth. 107 (1891) 

135-. 
Irregular determinants, formation. Perott, J. 

Crelle J. Mth. 95 (1883) 232-; 96 (1884) 

327-. 
and subtriplicate forms. Mathews, G. B. 

Mess. Mth. 20 (1891) 70-. 
Jacobian of functions, extension of theory. 

Gomes Teixeira, F. Mh. Mth. Ps. 1 (1890) 

481-. 
, property of the. Faa de Bruno, F. Am. 

J. Mth. 3 (1880) 154-. 
Jacobians, a proposition relating to. Peano, G. 

G. Mt. 27 (1889) 226-. 
Kronecker's linear relation among minors of 

symmetric determinant. White, H. S. 

N. Y. Am. Mth. S. Bll. 2 (1896) 136-. 
Lame", proof of theorem of. Trzaska, W. 

Par. T. Nauk. Sc. Pam. 10 (*1878) Art. 9, 

3 pp. 
Laplace's theorem for the distribution of a 

determinant, extension. Netto, E. Crelle 

J. Mth. 114 (1895) 345-. 
Linear forms and determinants. Mtray, C. 

Liouv. J. Mth. 10 (1884) 181-. 
, theorem on system of. Frattini, G. 
Km. B. Ac. Line. Bd. 2 (1886) (Sent. 1) 

Magic squares, relation to theory of deter- 
minants. Studnicka, F. J. Prag Sb. (1876) 
269-. 

Maximum modulus which a determinant can 
have. Hadamard, . C. B. 116 (1893) 
1500-. 



Determinants 2010 

Minor determinants. Janni, G. G. Mt. 1 

(1863) 270-. 
of an adjoint determinant. Hoza, F. 

Arch. Mth. Ps. 59 (1876) 401-. 
linearly equivalent quadratic functions, 

relation. Sylvester, J. J. Ph. Mg. 1 (1851) 

295-. 
symmetrical determinant, property. 

Hazzidakis, J. N. [1880] Crelle J. Mth. 

91 (1881) 238-. 
systems. Kronecker, L. Berl. Ak. 

Sb. (1882) 821-. 
. Mehmke, R. Mth. A. 26 

(1886) 209-. 

, linear relations. Runge, C. 
Crelle J. Mth. 93 (1882) 319-. 

, theory. Hoza, F. Arch. Mth. Ps. 

59 (1876) 387-. 

Minors of a determinant of Hankel, relations 
between. Cazzaniga, T. Mil. I. Lomb. Bd. 
31 (1898) 610-. 

, relation between. Vanecek, M. N. 

Prag Sb. (1886) (Mth.-Nt.) 21-. 

, law of extensible. Muir, T. [1881] 
Edinb. B. S. T. 30 (1883) 1-. 

, principal, of a symmetrical determinant. 
Schultze, E. Bll. Sc. Mth. As. 10 (1876) 
242-. 

Multinomial determinant. Segar, H. W. 
Mess. Mth. 21 (1892) 177-. 

Multiple determinants, properties. Deruyts, J. 
Liege S. Sc. Mm. 9 (1882) (No. 7) 11 pp. 

Multiplication of trigonometric and hyperbolic 
functions. Trzaska, W. Par. T. Nauk 
Sc. Pam. 10 (*1878) Art. 8, 7 pp. 

Normal determinants, reciprocals of. Caz- 
zaniga, T. Tor. Ac. Sc. At. 34 (1898) 351- 
or 495-. 

Numerical determinant, calculation. Cazza- 
niga, T. G. Mt. 36 (1898) 362-. 

, sign of term, rule. Mainardi, G. 
Mil. At. I. Lomb. 1 (1858) 105-. 

0, a certain differential, determinantal operator. 

Vivanti, G. Palermo Cir. Mt. Bd. 4 (1890) 

261-. 
Orders of conditions that minors of different 

degree of given matrix may vanish. Segre, C. 

Bm. B. Ac. Line. Bd. 9 (1900) (Sem. 2) 253-. 
Orthogonal substitutions. Jacobi, C. G. J. 

Crelle J. 15 (1836) 309-. 
Orthogonants, property. Loria, G. G. Teix. 

J. Sc. 7 (1886) 129-. 
, theory. Netto, E. Acta Mth. 19 (1895) 

105-. 
Orthosymmetric determinants. Brunn, H. 

Z. Mth. Ps. 37 (1892) 291-. 
Partial compounds. Nansoii, E. J. Mess. 

Mth. 28 (1899) 17-. 

determinants, theorem of Jacobi, generali- 
sation. Barbier, E. C. B. 97 (1883) 
82-. 

differentials as determinants. Gubkin, I. S. 
[1880] Mosc. S. Sc. Bll. 73 (No. 1) (1891) 
29-. 

Pascal's triangle, certain of whose elements 
constitute a determinant, properties of 
latter. Pincherle, S. G. Mt. 19 (1881) 385-. 



134 



2010 Determinants 

Permanents and determinants, relation. Muir, 

T. [1897] Edinb. B. S. P. 22 (1900) 

134-. 
Persymmetric determinants. Muir, T. [1881] 

Mess. Mth. 11 (1882) 65-. 
Pfaffian having a vacant minor, development. 

Muir, T. [1900] Edinb. E. S. T. 40 (1905) 

49-. 
Poisson's determinants. Albeggiani, M. L. 

Palermo Cir. Mt. Ed. 1 (1887) 6-. 
generalised. Albefigiani, M. L. Palermo 

Cir. Mt. Ed. 1 (1887) 9-, 12-, 314-. 
Potential determinants, mutual relations. 

Jonquieres, de. C. E. 120 (1895) 408-, 

580. 
"Power" and "combination" determinants. 

Studnicka, F. J. Prag Sb. (1897) (Mth.-Nt.) 

No. 1, 20pp., No. 16, 16pp. 
determinants. Stiidnicka, F. J. Casopis 

26 (1897) 105- ; Fschr. Mth. (1897) 142-. 
[SMi 2 - )] StudnUka, F. J. Prag 

Sb. (1896) (Mth.-Nt.) No. 22, 8 pp. 
Powers and determinants, relation. Giinther, 

S. Z. Mth. Ps. 24 (1879) 244-. 
Product of 2 determinants, decomposed. 

Solution of theorem of Sylvester's. Faa 

de Bruno, F. [1851] Liouv. J. Mth. 17 

(1852) 190-. 
Eeciprocal determinants. Gruzincev, A. P. T, 



Determinants 2010 

Simple alternants. Muir, T. [1887] Edinb. 

E. S. P. 14 (1888) 433-. 
, class. Muir, T. [1888] Edinb. E. S. 

P. 15 (1889) 298-. 
Skew determinant of infinite order, mean value 

of numerical coefficients. Sylvester, J. J. 

C. E. 89 (1879) 497-. 
determinants. Cayley, A. Crelle J. 32 

(1846) 119- ; 38 (1849) 93-. 
. Brioschi, F. Liouv. J. Mth. 19 (1854) 

253-. 
. Hermite, C. Camb. and Dubl. Mth. 

J. 9 (1854) 63-. 
. Cayley, A. Crelle J. 50 (1855) 277-; 

55 (1858) 277-. 

. Muir, T. Ph. Mg. 12 (1881) 391-. 

. Mertens, F. Wien Ak. Sb. 96 (1888) 

(Ab. 2) 1245-. 
. Cazzaniga, T. Mil. I. Lomb. Ed. 30 

(1897) 1303-. 
, Cayley's theory applied to displacement 

of rigid system about a fixed origin. Schl&fti, 

L. [1865] QJ. Mth. 8 (1867) 167-. 
of higher dimensions. Gegenbauer, L. 

Wien Ak. D. 55 (1889) (Ab. 1) 39-. 
, history. Muir, T. [1900] Edinb. E. S. 

P. 23 (1902) 181-. 

partly zero-axial, condensation. Muir, 
L. Mth. - 



Kharkov Mth. S. Com. 3 (1893) 94-; Fschr. 

Mth. (1891) 147. 
. Musso, G. G. Mt. 31 (1893) 201- ; 

32 (1894) 81-. 
Eegular determinants and derived systems. 

Hensel, K. Crelle J. Mth. 114 (1895) 25-. 
Eesolution of a determinant into quadratic 

factors. Muir, T. [1881] Mess. Mth. 11 

(1882) 105-. 
determinants, general problem. Giinther, 

S. Arch. Mth. Ps. 59 (1876) 130-. 
, new method. Teixeira, J. P. G. 

Teix. J. Sc. 11 (1892) 173-. 
linear equations, method, and application 

to determinants. Clasen, (I'abbe) B. I. 

Brux. S. Sc. A. 12 (1888) (Pt. 2) 251-. 
Screws, theory of, note on determinant in. 

Ball, (Sir) E. S. [1890] Ir. Ac. P. 1 (1889-91) 

375-. 
Semi-determinants. Scheibner, W. Leip. B. 

11 (1859) 151-. 
-symmetrical determinants of even order. 

Le Paige, C. M. M. H. H. Prag Sb. (1880) 

125-. 
Sets of integers whose determinant is > or 

<1. Hermite, C. Liouv. J. Mth. 14 (1849) 

21-. 
Sign of any term of a determinant. Zehfuss, 

G. (xi) Z. Mth. Ps. 3 (1858) 247-, 249-. 
. Johnson, W. W. [1876] 

Mess. Mth. 7 (1878) 59. 
. Tanner, H. W. L. 

[1879] Mess. Mth. 9 (1880) 51-. 
. Perry, H. M. (xn) 

[1881] J. H. Un. Cir. [1] (1882) 151. 
. Muir, T. [1899] 

Edinb. E. S. P. 22 (1900) 441-. 
, short rule for. Jenkins, 

M. Mess. Mth. 25 (1896) 60-. 



i. S. P. 13 (1881-82) 161-. 



, property. Hill, M. J. M. L. Mth. S. 

P. 26 (1895) 341-. 

or symmetric determinant of infinite order, 
mean value of coefficients in development of. 
Sylvester, J. J. C. E. 89 (1879) 24-. 

symmetric determinants. Janni, G. G. 
Mt. 1 (1863) 275-. 

, property. Deruyts, F. Liege S. Sc. 

Mm. 17 (1892) No. 2, 6 pp. 
Stieltjes' theorem, twofold generalisation. 

Taber, H. L. Mth. S. P. 27 (1896) 

613-. 
Sturm's functions, coefficients expressed as 

determinants. Heal, W. E. A. Mth. 2 

(1885-86) 85-. 
, determination of a series from a single 

determinant. Vleck, E. B. van. [1399] 

A. Mth. 1 (1900) 1-. 
Sums of determinants. Deruyts, J. Liege S. 

Sc. Mm. 10 (1883) (No. 4) 11 pp. 
powers of natural numbers, representation 

by determinants. Siacci, F. A. Mt. 7 

(1865) 19-. 
Sylvester's determinant. Hesse, L. O. Tor- 

tolini A. 2 (1359) 5-. 

, transformation to Cauchy's. Biehler, 
C. N. A. Mth. 19 (1880) 110- . 

Symbol analogous to determinants. Ferber, 
. Par. S. Mth. Bll. 27 (1399) 285-. 

of positive determinants, application. 
Ferber, . Par. S. Mth. Bll. 28 (1900) 
128-. 

Symbolic determinants. Rusjan, C. K. Fschr. 

Mth. (1899) 315. 
Symmetric determinant connected with 

Lagrange's interpolation problem. Muir, 

T. L. Mth. S. P. 13 (1881-82) 156-. 
, number of terms. Cayley, A. As. S. 

M. Not. 34 (1874) 303-, 335. 



135 



2010 Determinants 

Symmetric determinant, special. Geftenbauer, 
L. [1880] Wien Ak. Sb. 82 (1881) (Ab. 2 
938-. 

, , note. Muir, T. Des Moines Anal. 

8 (1881) 169-. 

determinants. Mertens, F. Crelle J. Mth. 
82 (1877) 207-. 

, class. Noether, M. Mth. A. 16 (1880) 

551-. 
, , and its use in continued fractions. 

Studnicka, F. Prag Sb. (1872) 74-. 
, new properties. Muir, T. QJ. Mth. 

18 (1882) 166-. 

, theorem relating to. Buchheim, A. 
Mess. Mth. 14 (1885) 143-. 

forms of determinants. Scott, R. F. Mess. 
Mth. 8 (1879) 131-, 145-. 

, skew-symmetric, and orthogonal matrices, 
properties. Taber, H. L. Mth. S. P. 22 
(1891) 449-. 

, , , . Metzler,W.H. Am. 

J. Mth. 15 (1893) 274-. 

Systems of moduli applied to theory of deter- 
minants. Kronecker, L. Crelle J. Mth. 107 
(1891) 254-. 

Three-dimensional determinants. Hedrick, E, 
E. [1899] A. Mth. 1 (1900) 49-. 

Transformable system, determinant of a. 
Deruyts, J. Brux. Ac. Bll. 32 (1896) 433-. 

Transformation of determinant into any equi- 
valent determinant. Van Velzer, C. A. 
Des Moines Anal. 9 (1882) 116-. 

. Muir, T. Des Moines 

Anal. 10 (1883) 8-. 

continuant. Muir, T. [1881] 

Edinb. E. S. T. 30 (1883) 5-. 

. Chrystal, G. [1881] Edinb. 

E. S. T. 30 (1883) 13-. 

determinants in conic sections. Caspary, 

F. [1880] Crelle J. Mth. 92 (1882) 123-. 
, mode of. Fouret, G. Par. S. Mth. 

Bll. 14 (1886) 146- . 

, proof. Fiore, V. G. Mt. 10 (1872) 

170. 

formulae. Rubini, R. G. Mt. 16 (1878) 
198-, 344. 

, a new. Studnicka, F. J. Prag Sb. (1879) 
489-. 

of product of determinants, Sylvester's 
theorem, note. Sperling, J. F. de. Liouv. 
J. Mth. 5 (1860) 121-. 

rectangular coordinates. Janse, L. (Bz.) 

N. Arch. Wisk. 12 (1886) 109- ; Fschr. Mth. 
(1885) 676.' 

Transformations of determinants. Siacci, F. 
[1872] A. Mt. 5 (1871-73) 296-. 

Triangle, application of determinants to geo- 
metry of. Avillez, J. F. d' (Visconde de 
Reguengo). [1897] Lisb. J. Sc. Mth. 5 
(1898) 14-. 

, determinant giving area in terms of sides. 
Ritsert, E. Z. Mth. Ps. 17 (1872) 513-. 

Two-step determinants, theorem. Torelli, G. 
. G. Mt. 4 (1866) 294-. 

Uni-modular determinant, construction. 
Weihrauch, K. Z. Mth. Ps. 21 (1876) 134-. 

Vanishing aggregates of determinants. Muir, 
T. [1888] Edinb. E. S. P. 15 (1889) 96-. 



Discriminants and Resultants 2020 

Wronskian determinant. Peano, G. Mathesis 

9 (1889) 75-, 110- ; Em. E. Ac. Line. Ed. 6 

(1397) (Sem. 1) 413-. 
. Vivanti, G. Em. E. Ac. Line. Ed. 7 

(1898) (Sem. 1) 194-. 
, generalisation of properties. Pincherle, 

S. Em. E. Ac. Line. Ed. 6 (1897) (Sem. 1) 

301-. 
, . Bortolotti, E. Em. E. Ac. 

Line. Ed. 7 (1898) (Sem. 1) 45-. 

determinants. Lecornu, L. As. Fr. C. E. 
(1894) (Pt. 2) 282-. 

, properties and some applications. 
Dickstein, S. Prace Mt.-Fiz. 1 (1888) 5-; 
Fschr. Mth. (1888) 151. 

Wronskians, fundamental property. Demoulin, 

A. Mathesis 17 (1897) 62-. 
Zero-determinants of infinite order. Cazzaniga, 

T. A. Mt. 1 (1898) 83-. 

2020 Discriminants and 
resultants. 

Algebraic aggregate, discriminant. Hensel, K. 

Gott. Nr. (1897) 247-. 
, fundamental equation, and non-essential 

factors of the discriminant. Hensel, K. 

Gott. Nr. (1897) 254-. 

equivalences and elimination. Laurent, H. 
N. A. Mth. 5 (1886) 432-, 456-. 

resolvents. Rados, G. Mth. Termt. Ets. 
17 (1899) 421- ; Mth. Nt. B. Ung. 18 (1903) 
236-. 

C-discriminant as an envelope. Macdonald, 

J. A. Edinb. E. S. T. 39 (1900) 27-. 
Continuant, the discriminant of a special 

quadratic form. Cesdro, E. Mathesis 12 

(1892) 5-. 
Determinantal equation connected with small 

oscillations, etc. Muir, T. Mess. Mth. 14 

(1885) 141-. 

, Lagrange's. Muir, T. Ph. Mg. 43 
(1897) 220-. 

, , Sylvester's proof of the reality of the 

roots of. Muir, T. Am. J. Mth. 19 (1897) 
31 2-. 

, reciprocity of roots (Brioschi's theorem). 

Faa de Bruno, F. Liouv. J. Mth. 19 (1854) 
304. 

Determination of common roots of given equa- 
tions by means of their eliminant. Baraniecki, 
M. A. Par. T. Nauk Sc. Pam. 10 (*1878) 
Art. 5, 7 pp. 

Discriminant of cubic giving axes of a quadric 
surface, decomposition into sum of squares. 
Bauer, G. [1868] Crelle J. Mth. 71 (1870) 
40-. 

, degree with respect to a parameter. 
Roberts, E. [1869] QJ. Mth. 10 (1870) 
204-. 

of finite hypergeometric Beries. Hilbert, D. 
Crelle J. Mth. 103 (1888) 337-. 

general quadratic. Dupuis, N. F. Cn. 

E. S. P. & T. 7 (1890) (Sect. 3) 15-. 

Jacobians of three quadratic forms. 
Igel, B. [1876] Wien Ak. Sb. 74 (1877) 
(Ab. 2) 355-; 75 (1877) (Ab. 2) 830-. 



136 



2020 Discriminants and Resultants 

Discriminant of quadratic forms, property. 
Picquet, H. As. Fr. C. E. (1875) 225-. 

quartic equation. Weill, M. N. A. 
Mth. 2 (1883) 265-. 

quaternary quadratic form, properties. 
Walker, J. J. [1865] Mess. Mth. 4 (1868) 
25-, 187-. 

, special. Cayley, A. QJ. Mth. 11 (1871) 
211-. 

surfaces of algebraic equations, coefficients 
being coordinates. Czuber, E. Mh. Mth. 
Ps. 5 (1894) 62-. 

, transformation of characteristic equations 

by. BrioscM, F. Tortolini A. 7 (1856) 64-. 
Discriminantal equation, roots. Brisse, C. 

N. A. Mth. 9 (1890) 367-. 
Discriminants. Bellavitis, G. Yen. At. (1858- 

59) 65-, 82-. 

. Brill, A. Mth. A. 12 (1877) 87-. 
. Casorati, E. Mil. I. Lomb. Ed. 18 

(1885) 108-. 

of algebraic equations, factorisation of. 
Netto, E. Mth. A. 24 (1884) 579-. 

functions of one variable. Kronecker, 

L. Crelle J. Mth. 91 (1881) 301-. 
, arithmetical researches on non-essential 

factors of. Kernel, K. Crelle J. Mth. 113 

(1894) 128-. 
, forms of, theorem. Kronecker, L. Crelle 

J. Mth. 100 (1887) 79-. 
, formulae, and application to discriminants 

of discriminants, and to polar curves. 

Henrici, 0. [1868] L. Mth. S. P. 2 (1869) 

104-. 
, invariants, covariants, and hyperdetenni- 

nants, elementary notions. Terquem, O. 

N. A. Mth. 18 (1859) 249-, 299-, 446-. 

of resultants. Brill, A. Gott.' Nr. (1889) 
89-. 

and resultants of equations for singularities. 
Meyer, F. Gott. Nr. (1888) 74-; (1890) 
366-, 493-; (1891) 14-. 

, theorem. Sylvester, J. J. E. S. P. 14 
(1865) 336-. 

, theory. Netto, E. Crelle J. Mth. 90 
(1881) 164- ; Acta Mth. 1 (1882) 371-. 

Discriminating cubic ; representation of dis- 
criminant as sum of squares. Tannery, J. 
Bll. Sc. Mth. As. 7 (1883) (Pt. 1) 103-. 

determinant equations, reality of roots of. 
Elliott, E. B. QJ. Mth. 31 (1900) 233-. 

equation (formed from symmetric deter- 
minant), properties. Kaiser, . D. Nf. 
Tbl. (1887) 228. 

equation, reality of roots of, when deter- 
minant is not symmetric. Bendixson, I. 
Stockh. Ofv. (1900) 1099-. 

Divisibility, notion including, and general theory 
of elimination. Molk, J. Acta Mth. 6 
(1885) 1-. 



Eliminant of 



). Muir, T. 



[1896] Edinb. E. S. P. 21 (1897) 360-. 
, persymmetric. Muir, T. [1899] Edinb. 

B. S. P. 22 (1900) 543-. 
of set of quaternary quadrics. Muir, T. 

[1896] Edinb. E. S. P. 21 (1897) 328-. 



Elimination 2020 

Eliminant of set of ternary quadrics. Muir, T. 

[1896] Edinb. E. S. P. 21 (1897) 220-. 
or quaternary quadrics. Nanson, 

E. J. [1899] Edinb. E. S. P. 22 (1900 

353-. 
, Sylvester's, form. Gordon, P. D. Nf. 

Vh. (1893) (Th. 2, Halfte 1) 4. 

of system of equations, degree. Vahlen, 
K. T. Crelle J. Mth. 113 (1894) 348-. 

, formation. Biermann, 0. Mh. 

Mth. Ps. 5 (1894) 17-. 

two equations. Mansion, P. Brux. S. 
Sc. A. 18 (1894) (Pt. 1) 5-. 

, degree. Janni, V. G. Mt. 12 

(1874) 27. 
, . Lachlan, R. Camb. Ph. S. 

P. 9 (1898) 313-. 
, dialytic form. Sylvester, J. J. 

Ph. Mg. 16 (1840) 132-. 
Eliminants and associated roots. Elliott, E. B. 

L. Mth. S. P. 16 (1884-85) 224-. 
, Sylvester's and Cauchy's, equality. 

Mansion, P. [1879] Mess. Mth. 9 (1880) 

60-. 

Elimination. 

Poisson, S. D. Par. EC. Pol. J. 4 (1801-2) 

(11" cah.) 199-. 

Badano, . Geneva Mm. Ac. 3 (1814) 125-. 
Babbage, C. QJ. Sc. 3 (1817) 355-. 
Poncelet, J. V. Gergonne A. Mth. 8 (1817-18) 

201-. 
Gergonne, J. D. Gergonne A. Mth. 21 (1830- 

31) 41-. 
Murphy, E. [1832] Camb. Ph. S. T. 5 (1835) 

65-. 

Sylvester, J. J. Ph. Mg. 17 (1840) 379-. 
Liouville, J. Liouv. J. Mth. 6 (1841) 345-. 
Terquem, 0. N. A. Mth. 1 (1842) 125-. 
Moon, E. Camb. Mth. J. 3 (1843) 183-. 
Finck, B. Liouv. J. Mth. 9 (1844) 334-. 
Bouillon, . N. A. Mth. 4 (1845) 120-. 
Cockle, Jas. Ph. Mg. 27 (1845) 292-. 
Cayley, A. Crelle J. 34 (1847) 30-. 
Crelle, A. L. Crelle J. 43 (1852) 37-. 
Genocchi, A. N. A. Mth. 14 (1855) 259-. 
Cayley, A. [1861] Crelle J. 60 (1862) 373-. 
Lemonnier, H. C. E. 80 (1875) 252-. 
Eouche-, E. N. A. Mth. 16 (1877) 105-. 
Lemonnier, H. Par. EC. Norm. A. 7 (1878) 

77-, 151-. 
Mansion, P. C. E. 87 (1878) 975- ; Brux. Ac. 

Bll. 46 (1878) 899-; 47 (1879) 532-; 48 

(1879) 463-, 473-. 
Le Paige, C. M. M. H. H. C. E. 90 (1880) 

1210-. 

Biehler, C. N. A. Mth. 1 (1882) 529-. 
Laurent, H. N. A. Mth. 11 (1892) 5-. 
Worontzoff, . N. A. Mth. 11 (1892) 291-. 
Laurent, H. N. A. Mth. 12 (1893) 355-. 
Hadamard, J. C. E. 119 (1894) 995-, 1243 ; 

Acta Mth. 20 (1897) 201-. 
Netto, E. Giessen Oberh. Gs. B. 32 (1897-99) 

78-. 
Bezout-Cauchy method. Falk, M. Ups. S. 

Sc. N. Acta 10 (1879) No. 15, 36 pp. 
. Hioux, V. N. A. Mth. 18 (1879) 289-. 



137 



2020 Elimination 

Bezout's method. Cayley, A. Crelle J. 53 

(1857) 366-; Mess. Mth. 2 (1863) 88-. 
. Painvin, L. N. A. Mth. 13 (1874) 

278-. 
. Stickelberger, . D. Nf. B. (* 1883) 

58. 
and continued fractions. Borchardt, C. W. 

Berl. Ak. Ab. (1878) (Mth. 1-). 
by cross-multiplication. Smith, Arch. Camb. 

Mth. J. 1 (1839) 46. 
degree of equation resulting from. Minding, 

E. F. A. Crelle J. 22 (1841) 178-. 
. Magnus, L. J. Crelle J. 26 

(1843) 365-. 

- , expression for. Minding, 
E. F. A. [1843] St Pet. Ac. Sc. Bll. 2 

(1844) 273-. 

dialytic method. Sylvester, J. J. Ir. Ac. P. 2 

(1840-44) 130-. 
applied to ternary systems of equations. 

Sylvester, J. J. Camb. Mth. J. 2 (1841) 

232-. 
, extensions. Sylvester, J. J. Ph. Mg. 2 

(1851) 221-. 
, Sylvester's. Madsen, (Kapt.) V. H. 0. 

(xn) Ts. Mth. 5 (1875) 144-. 
in equations of 1st order. Gergonne, J. D. 

Gergonne A. Mth. 4 (1813-14) 148- ; 12 

(1821-22) 281- ; 20 (1829-30) 109-. 
. Majo, L. de. Nap. Mm. Ac. 

Sc. 1 (1852-54) 101-. 
by finding common divisor. 

Raymond, G. M. Gergonne A. Mth. 2 

(1811-12) 38-. 
higher orders. Kramp, C. Gergonne 

A. Mth. 1 (1810-11) 321-. 
Euler's method. Biehler, C. N. A. Mth. 6 

(1887) 67-. 
example. Anderson, Jas. Mathematician 1 

(1845) 181-. 

formation of eliminant. Bes, K. Amst. Ak. 

Vs. 8 (1900) 173- ; Amst. Ak. P. 2 (1900) 

85-. 
formula. Cayley, A. L. Mth. S. P. 11 (1879- 

80) 139-. 
Gauss's method. Hall, A. A. Mth. 8 (1893- 

94) 64. 
general theory. Voizot, . L'l. 3 (1835) 

.' Bes, K. Amst. Ak. Vh. (Sect. 1) 6 

(1899) No. 7, 121 pp. 
by H.C.F. Bret, . Par. EC. Pol. J. 8 

(1809) (15 e cah.) 162- ; Gergonne A. Mth. 3 

(1812-13) 13-. 
. Sarrus,F. (vi Adds.) Strasb. S. 

Sc. N. Mm. 2 (1832) 190-. 

indeterminate multipliers. Smith, Arch. 
Camb. Mth. J. 1 (1839) 49-. 

introduction to a theory. Garbieri, G. G. 
Mt. 30 (1892] 41-. 

linear method for algebraic equations. 
Sylvester, J. J. Ph. Mg. 18 (1841) 425-. 

and linear simultaneous equations, algebraic or 
differential. Mainardi, G. Mil. At. I. 
Lomb. 1(1858) 95-. 

Liouville's theorem, demonstration and ap- 
plication. Fouret, G. N. A. Mth. 9 (1890) 



Elimination 2020 

method. Craufitrd, A. Q. G. Camb. Mth. J. 

2 (1841) 276-. 

. Cayley, A. N. A. Mth. 18 (1859) 
397-. 

of obtaining final equation without irrelevant 
factors. Araldi, A. (ix) [1858] Mod. Ac. 
Sc. Mm. 3 (1861) 3-. 

methods. Cossali, P. [1812] Mod. Mm. S. 
It. 16 (1813) 272-. 

of Fontaine, Vandermonde, and Laplace. 
Terquem, O. N. A. Mth. 5 (1846) 153-. 

new and extended theory. Sylvester, J. J. 

Ph. Mg. 15 (1839) 428-; 16 (1840) 37-. 
and polars. Clebsch, A. [1860] Crelle J. 58 

(1861) 273-. 
problem. Borchardt, C. W. Berl. Mb. (1859) 

376-. 

. Krey, H. Mth. A. 12 (1877) 476-. 
. Stephanos, C. C. B. 97 (1883) 1050-. 

comprising theory. Ventejols, . C. B. 
84 (1877) 546-. 

of Sylvester's. Tait, . [1892] Edinb. B. 
S. P. 19 (1893) 131-. 

. Muir, T. [1892] Edinb. B. S. P. 

20 (1895) 300-. 
. Cayley,. [1894] Edinb. B. S. P. 

20 (1895) 306-. 
. Muir, T. Edinb. B. S. P. 20 

(1895) 371-. 
. Nanson, E. J. [1897] Edinb. B. S. 

P. 22 (1900) 150-. 
problems. Cayley, A. QJ. Mth. 8 (1867) 

183- ; 11 (1871) 99-. 
on curves satisfying given conditions. 

Brill, A. Gott. Nr. (1870) 525-. 
a process in. Biehler, C. N. A. Mth. 19 (1880) 

202-, 332-. 
between quadratic and set of linear functions 

(reply to Boole). Sylvester, J. J. Camb. 

and Dubl. Mth. J. 6 (1851) 171-. 

quadratics, theorems in. Sylvester, J. 7. 
Ph. Mg. 37 (1850) 213-. 

result. Salmon, G. Camb. and Dubl. Mth. J. 

3 (1848) 169-. 

. Cayley, A. Tortolini A. 7 (1856) 454-. 
resultants, comparison. Borchardt, C. W. 

Crelle J. 57 (1860) 183-. 
simple. Drinkwater, J. E. Ph. Mg. 10 (1831) 

24-. 
by special algorithm. Gruson, J. P. Berl. 

Ab. (1816-17) 1-. 
symbolic process. Clebsch, A. Berl. Mb. 

(1860) 536-. 
by symmetric functions. Liouville, J. N. A. 

Mth. 6 (1847) 295-. 
symmetrical method in simple equations by 

determinants. Warner, J. D. Am. As. P. 

(1881) 50-. 
from a system of equations. Brill, A. [1871] 

Mth. A. 5 (1872) 378-. 

theorem. Cayley, A. QJ. Mth. 12 (1873) 5-. 
theory. Eichelot, F. J. Crelle J. 21 (1840) 

226-. 
. Grunert, J. A. Grunert Arch. 2 (1842) 

76-, 337-, 345-. 
. Crelle, A. L. Berl. Ab. (1844) 1- ; (1845) 

1-. 
. Chio, F. Palomba Bac. 3 (1847) 193-. 



138 



2020 Elimination 



Discriminants and Resultants 2020 



theory. Cayley, A. Camb. and Dubl. Mth. 

J. 3 (1848) 116-. 

. Salmon, G. QJ. Mth. 7 (1866) 327-. 
. ArzeKi, C. [1876] G. Mt. 15 (1877) 62-, 

. Noether, M. [1876] Erlang. Ps. Md. S. 

Sb. 9 (1877) 66-. 

. Toeplitz, J. Z. Mth. Ps. 23 (1878) 61-. 
. Laurent, H. N. A. Mth. 2 (1883) 145-. 
. Netto, E. Acta Mth. 7 (1885) 101-. 
. Schmidt, C. Z. Mth. Ps. 31 (1886) 214-. 
. Schendel, L. Z. Mth. Ps. 32 (1887) 46-. 
. Laurent, H. N. A. Mth. 7 (1888) 60-, 116-. 
. Loria, G. G. Teix. J. Sc. 9 (1889) 33-. 
. Kretkmvski, W. Prace Mt.-Fiz. 2 (1890) 

21- ; Fschr. Mth. (1890) 174-. 
. Pleskot, A. Prag Ceske Ak. Fr. Jos. Ez. 

(Tfida 2) 5 (1896) Art. 25, 13 pp.; Fschr. 

Mth. (1896) 91. 
. Mertens, F. Wien Ak. Sb. 108 (1899) 

(Ab. 2 a) 1173-, 1344-. 
, and algebraic curves. Brill, A. Mth. A. 4 

(1871) 510-. 
, principle of projection in. Meyer, F. D. 

Nf. Vh. (1890) (Th. 2) 9-. 
transformation and canonical forms . Sylvester, 

J. J. Camb. and Dubl. Mth. J. 6 (1851) 

186-. 
of two arbitrary functions. Tanner, H. W. L. 

[1875] Mess. Mth. 5 (1876) 98-. 
between two equations. Valerius, B. Liege 

A. Ac. (1826-27) 75 pp. 
. Meyer, A. Quetelet Cor. Mth. 5 

(1829) 100-. 
. Jacobi, C. G. J. Crelle J. 15 

(1836) 101-. 
. Petersen, J. P. C. (xn) [1873] Ts. 

Mth. 4 (1874) 83-. 
. Zeuthen, H. G. (xn) Ts. Mth. 4 

(1874) 165-. 
. Cauchy, . N. A. Mth. 15 (1876) 

385-, 433-. 
. Forestier, C. Toul. Ac. Sc. Mm. 9 

(1877) 142-. 
. Mansion, P. Brux. Ac. Bll. 48 

(1879) 491-. 
. Kronecker, L. Berl. Ak. Mb. 

(1881) 535-. 
, application of indeterminate analysis. 

Wallace, (Prof.) W. Edinb. Ph. J. 1 (1819) 

29-. 
, final equation. Hesse, L. 0. Crelle 

J. 27 (1844) 1-. 
in one unknown. Darboux, G. (rx) 

Bll. Sc. Mth. As. 10 (1867) 56- ; 1 (1877) 54-. 

two unknowns. Vene, A. A. 
Brux. Mm. Cour. 4 (1824) (No. 2) 26 pp. 

. Finck, B. N. A. Mth. 4 

(1845) 198-. 
. of 2nd order. Horner, W. G. Ph. 

Mg. 5 (1834) 188-. 
,2 unknowns. Merlieux, E, 

N. A. Mth. 2 (1843) 34-. 
3rd order. Clebsch, E. F. A. 

[1864] Crelle J. 64 (1865) 95-. 

three equations of 2nd order. Hesse, L. 0. 
Crelle J. 28 (1844) 68-. 



Eliminations arising in trigonometry. Meyer, 

F. D. Mth. Vr. Jbr. 4 (1897) 92-. 
, equations resulting from various. Bezout, 

. N. A. Mth. 18 (1859) 120-. 
Equation for max. and min. of n-ary quadric. 

Gravelaar, N. L. W. A. N. Arch. Wisk. 4 

(*1878) 113-. 

of squares of differences. Brioschi, F. 
Tortolini A. 7 (1856) 5-. 

Equations whose discriminant is a square. 

Netto, E. Crelle J. Mth. 95 (1883) 237-. 
Gauss's method of substitution. Johnson, W. W. 

A. Mth. 7 (1892-93) 65-. 
Order of manifoldness arising from several 

linear systems. Fieri, M. Palermo Cir. 

Mt. Ed. 11 (1897) 58-. 
^-discriminant of differential equation of first 

order, and its connection with general theory 

of envelopes. Chrystal, . Edinb. E. S. 

T. 38 (1897) 803-. 
Power determinant, a. Jung, V. Casopis 29 

(1900) 41- ; Fschr. Mth. (1900) 157. 

determinants. Jung, V. Prag Ceske" Ak. 
Fr. Jos. Ez. (Tfida 2) 8 (1899) Art. 38, 
22 pp. ; Fschr. Mth. (1899) 153. 

Product of differences of roots of equations, 

relation of discriminants and resultants to. 

Sylvester, J. J. Mess. Mth. 9 (1880) 164-. 
Property of product of linear factors. Brioschi, 

F. Camb. and Dubl. Mth. J. 9 (1854) 137-. 
Eesultant of a covariant and a fundamental 

form. Kohn, G. Wien Ak. Sb. 100 (1891) 

(Ab. 2a) 1013-. 

, degree. Ise, E. G. Mt. 11 (1873) 253-. 
of elimination of z from algebraic equations 

f(z) = Q and <f>(z) = Q, new representation. 

Rosenhain, G. Crelle J. 30 (1846) 157-. 
, Euler's. Hesse, L. 0. Tortolini A. 2 

(1859) 5-. 

and G.C.M. of integral algebraical ex- 
pressions. Sziits, N. von. Mh. Mth. Ps. 9 
(1898) 34-. 

of integral functions. Biermann, 0. Mh. 
Mth. Ps. 2 (1891) 143-. 

multipartite system of equations, degree 

and "weight." Sylvester, J. J. E. S. P. 12 

(1862-63) 674-. 
n equations. Faa de Bruno, F. Tortolini 

A. 7 (1856) 222-. 
an jj-ic and of a cubic. Pascal, E. G. 

Mt. 25 (1887) 257-. 
, order of, case of evaporation. Clifford, 

W. K. [1870] L. Mth. S. P. 3 (1869-71) 80-. 

R of two forms of the mth and nth degrees, 
P.D.E. satisfied by. Gordon, P. Gott. Nr. 
(1870) 427-. 

, the reduced. Brill, A. Munch. Ak. Ab. 17 
(1892) 89-. 

of several algebraic equations. Laurent, H. 
N. A. Mth. 12 (1893) 305-. 

system of equations. Schlafli, L. Wien 

D. 4 (1852) (Ab. 2) 1-. 
(Schlafli). Cayley, A. Crelle 

J. 50 (1855) 277-. 
two equations. Cayley, A. [1857- 

67] Phil. Trans. 147 (1857) 703- ; 158 

(1868) 173-. 



139 



2020 Discriminants and Resultants 

Eesultant of two congruences. Sylvester, J. J. 
(xn) [1881] J. H. Un. Cir. [1] (1882) 131. 

equations. Brioschi, F. Creile J. 
53 (1857) 372-. 

. Ise,E.[1868] G. Mt. 8 (1870) 1-. 

. Gordon, P. Mth. A. 3 (1871) 

355-; C. E. 127 (1898) 539-. 
, application to twisted cubic curve. 

Waelsch, E. Mh. Mth. Ps. 2 (1891) 421-. 

, Brioschi's theorem. Fad de 
Bruno, F. Creile J. 64 (1857) 283-. 

of 4th order. Faa de Bruno, F. 

Tortolini A. 1 (1858) 362-. 

forms of the same order, new repre- 
sentation. Stahl, W. Mth. A. 35 (1890) 
395-. 

Eesultants. Vanecek, M. N. Prag Sb. (1888) 
(Mth.-Nt.) 152-. 

. Gordan, P. Mth. A. 45 (1894) 405-. 

, anastrophic. Cauchy, A. L. C. E. 44 
(1857) 370. 

corresponding to interpolation. Borchardt, 
C. W. Creile J. 57 (1860) 111-. 

of covariants. Gordan, P. Mth. A. 4 
(1871) 169-. 

, formation. Reuschle, C. Z. Mth. Ps. 30 

(1885) 106-. 
, note. Haskell, M. W. N. Y. Mth. S. Bll. 

1 (1892) 223-. 
, property. Brill, A. [1879] Mth. A. 16 

(1880) 345-. 

of quantics, determination of their numerical 
coefficients. Vanecek, M. N. Prag Sb. (1888) 
(Mth.-Nt.) 286-. 

, theorems. Igel, B. [1877] Wien Ak. Sb. 

76 (1878) (Ab. 2) 145-. 
.theory. Netto,E. Creile J. Mth. 116 (1896) 

33-; 117 (1897)57-. 
, , extension. Sylvester, J. C.E.58(1864) 

1074-, 1130, 1178-. 
, , note. Netto, E. Giessen Oberh. Gs. B. 

32 (1897-99) 37-. 

of two integral functions. Nagelsbach, H. 
Z. Mth. Ps. 17 (1872) 333-. 

, remark on property. Kowalew- 

ski, G. Arch. Mth. Ps. 17 (1900) 202-. 
, two, in theory of rectifiable compound 

logarithmic waves. Sylvester, J. J. Ph. 

Mg. 37 (1869) 375-. 
Eoots common to two complete equations. 

Hioux, V. Par. EC. Norm. A. 10 (1881) 

383-. 
equations. Abel, N. H. Gergonne 

A. Mth. 17 (1826-27) 204-. 
. Brioschi, F. N. A. Mth. 14 

(1855) 81-. 
. Garbieri, G. Catania Ac. 

Gioen. At. 6 (1893) Mm. 16, 9 pp. 
Sub-discriminant. Perrin, R. Liouv. J. Mth. 

10 (1894) 129-. 

Sylvester's problem of the three ternary equa- 
tions, new solution. McLaren, (Lord). 

Edinb. E. S. P. 19 (1893) 264-. 
Vanishing discriminant, application. Azza- 

relli, M. Tortolini A. 3 (1860) 16-. 
, applications to geometry. Azzarelli, M. 

Em. N. Line. At. 30 (1877) 290-. 



Linear Substitutions 2030 

2030 Characteristic properties of 
linear substitutions; types of 
linear substitutions. (See also 
1210.) 

"Adjoint" substitutions, theory. Rados, G. 

[1891] Mth. Termt. Ets. 10 (1892) 34-; 

Mth. Nt. B. Ung. 10 (1893) 98-. 
Analytic functions suitable to represent sub- 
stitutions. Dickson, L. E. Am. J. Mth. 18 

(1896) 210-. 

Bipartite quadric, automorphic linear trans- 
formation. Cayley, A. Phil. Trans. (1858) 

39-. 
, . Muir, T. Am. J. Mth. 20 

(1898) 215-. 
Canonical form, bi-orthogonal reduction of a 

lineo-linear form to. Sylvester, J. J. C. E. 

108 (1889) 651-. 
of linear homogeneous substitution in a 

Galois field. Dickson, L. E. Am. J. Mth. 

22 (1900) 121-. 
substitutions. Maschke, H. 

Mth. A. 50 (1898) 220-. 
a linear substitution of finite order. 

Burnside, W. Mess. Mth. 28 (1899) 111-. 

quadric, proof of reduction by real 
orthogonal substitution. Sylvester, J. J. 
Mess. Mth. 19 (1890) 1-. 

, reduction of a linear substitution to. 
Burnside, W. L. Mth. S. P. 30 (1899) 
180-. 

, . Dixon, A. C. [1899] 

L. Mth. S. P. 31 (1900) 170-. 
, .. Bromwich,T.J.PA. 

[1899] L. Mth. S. P. 31 (1900) 289-. 
Characteristic functions of substitutions. 

Cauchy, A. L. C. E. 21 (1845) 1254-. 
Equations containing linear functions of recti- 
linear coordinates. Dieu, T. N. A. Mth. 

4 (1865) 165-. 
Exchangeable linear substitutions. Amaldi, U. 

Mil. I. Lomb. Ed. 33 (1900) 731-. 
. Schlesinger, L. Creile J. Mth. 121 

(1900) 177-. 

substitutions, theory. Demeczky, . C. E. 
120 (1895) 39-. 

Induced linear substitutions. Franklin, F. 

Am. J. Mth. 16 (1894) 205-. 
. Rados, G. Mth. Termt. Ets. 16 

(1898) 378-; Mth. Nt. B. Ung. 16 (1899) 
241-. 

. Visnya, A. Mth. Nt. B. Ung. 16 

(1899) 187-. 

, groups. Rados, G. Mth. Termt. Ets. 

17 (1899) 44-; Mth. Nt. B. Ung. 17 (1901) 
227-. 

substitutions, rank of determinant in. 
Kurschdk, J. Mth. Termt. Ets. 18 (1900) 
44-; Mth. Nt. B. Ung. 18 (1903) 229-. 

Integral linear substitutions. Pick, G. Mth. 

A. 24 (1884) 588-. 
of determinant 1, composition of. 

Krazer, A. A. Mt. 12 (* 1883-84) 283-. 



140 



2030 



Linear Substitutions 



2030 



Integral linear substitutions not given by alge- 
braical congruences. Pick, G. Mth. A. 28 
(1887) 119-. 

Invariants of orthogonal substitutions (regarded 
as rotations). Schlafli, L. [1865] Crelle J. 
65 (1866) 185-. 

Inverse orthogonal matrices. Sylvester, J. J. 
Ph. Mg. 34 (1867) 461-. 

Kummer's configuration, and orthogonal sub- 
stitutions. Study, E. Leip. Mth. Ps. B. 
44 (1892) 122-. 

Linear orthogonal substitutions, special case. 
Stern, M. A. Crelle J. 67 (1867) 293-. 

substitutions. Polignac, C. de. Par. S. 
Mth. Bll. 4 (1876) 120- ; 5 (1877) 69-. 

. Poincare, H. C. E. 98 (1884) 349-. 

. Picard, E. C. E. 98 (1884) 416-. 

. Burnside, W. Mess. Mth. 22 " 

190-. 
, certain. Deruyts, J. Brux. Ac. Bll. 

24 (1892) 102-. 
, a property. Burnside, W. Mess. Mth. 

20 (1891) 163-. 

of a single variable with periodic 
coefficients. Ocagne, M. d'. Par. S. Mth. 
Bll. 19 (1891) 37-. 

, special groups of. Fricke, R. Mth. A. 

38 (1891) 50-, 461-. 

, theory. Netto, E. Acta Mth. 17 (1893) 

265-. 

, . Loeicy, A. Mth. A. 48 (1897) 97-; 

49 (1897) 448-. 

, , new. Laurent, H. N. A. Mth. 15 

(1896) 345-. 

by which a quadratic ternary form re- 
produces itself. Tannery, J. Bll. Sc. Mth. 
As. 11 (1876) 221-. 

transformations. Cayley, A. Camb. Mth. 
J. 4 (1845) 193- ; Camb. and Dubl. Mth. J. 
1 (1846) 104-. 

, some properties. Deruyts, J. Brux. 
Ac. Bll. 16 (1888) 576-. 

Orthogonal and Boolian invariant systems, 
. symbolism for. MacMahon, (Maj.) P. A. 

B. A. Ep. (1900) 647. 
, related, substitutions. Igel, B. [1877] 

Wien Ak. D. 39 (1879) (Ab. 2) 29-. 

substitution, properties of coefficients. Bar- 
delli, G. Mil. I. Lomb. Ed. 9 (1876) 167-. 

substitutions. Grunert, J. A. Arch. Mth. 
Ps. 44 (1865) 478-. 

. Gundelftnger, S. Crelle J. Mth. 99 

(1886) 147-. 

. Netto, E. Acta Mth. 9 (1887) 295-. 

. Catalan, E. As. Fr. C. E. (1893) 

(Pt. 2) 19-. 
. Taber, H. N. Y. Mth. S. Bll. 3 (1894) 

251-. 
. Rados, G. Mth. Termt. Ets. 18 (1900) 

128- ; Mth. Nt. B. Ung. 18 (1903) 231-. 
, conditions among coefficients. Rados, G. 

Mth. Termt. Ets. 16 (1898) 123- ; Mth. Nt. 

B. Ung. 16 (1899) 236-. 
with determinant ( - 1). Weill, G. Par. 

EC. Norm. A. 11 (1894) 23-. 
, equation connected with. Borsch, A. 

Z. Mth. Ps. 24 (1879) 391-. 



Orthogonal substitutions in involution. Prym, 

F. Gott. Ab. 38 (1892) (Mth.) 42 pp. 
, parametric expression of coefficients. 

Hunyady, J. Mag. Tud. Ak. Etk. (Mth.) 

14 (1892) No. 2, 43 pp., No. 3, 14 pp.; Mth. 

Nt. B. Ung. 7 (1890) 233-. 
and regular divisions of space. Goursat f 

E. C. E. 106 (1888) 1786- ; Par. EC. Norm. 

A. 6 (1889) 9-. 
(single alternate substitution). Taber, H. 

Am. J. Mth. 16 (1894) 123-. 
, theory. Voss, A. E. Mth. A. 13 (1878) 

320-. 
, . Rados, G. Mth. Termt. Ets. 10 

(1892) 16-; Mth. Nt. B. Ung. 10 (1893) 95-. 

system in parallel arrangement. Voss, A. 
Mth. A. 24 (1884) 48-. 

systems. Kronecker, L. Berl. Ak. Sb. 
(1890) 525-, 601-, 691-, 873-, 1063-. 

Powers and roots of linear substitutions. Syl- 
vester, J.J. C. E. 94 (1882) 55-. 

Quadratic form, automorphic transformation. 
Rosanes, J. Crelle J. Mth. 80 (1875) 52-. 

, transformations. Jordan, C. Liouv. 

J. Mth. 4 (1888) 349-. 

, . Loewy, A. Ac. Nt. C. N. Acta 

65 (1896) 1-. 

. , orthogonal transformation to sum of 
squares. Kneser, A. Arch. Mth. Ps. 15 
(1897) 225-. 

, reduction. Timerding, H. E. Crelle J. 

Mth. 122 (1900) 172-. 
, to squares : equation | a^k + S \ = 0. 

Walecki, . N. A. Mth. 1 (1882) 401-, 

556-. 
, transformation. Enneper, A. Z. Mth. 

Ps. 9 (1864) 358-. 

, to sum of squares. Hesse, L. 0. 
Crelle J. 45 (1853) 93-; 57 (1860) 175-. 

, . Gundelfinger, S. [1880] 

Crelle J. Mth. 91 (1881) 221-. 
, . Zajaczkowski, W. (xn) 

[1883] Krk. Ak. (Mt.-Prz.) Pam. 9 (1884) 1- ; 

Fschr. Mth. (1884) 165-. 
, . . Presle, de. Par. S. 

Mth. Bll. 14 (1886) 98-. 

, , Gauss's method. 
Somoff, J. St. Pet. Ac. Sc. Bll. 18 (1873) 
442-. 

forms and the discriminantal equation. 
Laurent, H. N. A. Mth. 10 (1891) 60S-. 

, reduction to least number of terms, 
Jacobi, C. G. J. Berl. B. (1848) 414-. 

, and transformation. Jordan, C. 
Liouv. J. Mth. 19 (1874) 397-. 

, removal of product terms from two. 
Jacobi, C. G. J. Crelle J. 12 (1834) 1-. 

, simultaneous transformation. Cayley, A . 

Camb. and Dubl. Mth. J. 4 (1849) 47-; QJ. 

Mth. 2 (1858) 192-. 
, . Siacci, F. Tor. At. Ac. Sc. 

7 (1871-72) 758-. 
, theory. Jamet, V. Mars. Fac. Sc. A. 

10 (1900) Fasc. 5, 18 pp. 
, transformation. Smith, Arch. Camb. 

Mth. J. 1 (1839) 272-. 
, . Cayley, A. Crelle J. 50 (1855) 277-. 



141 



2030 Linear Substitutions 

Quadratic forms, transformation. Trudi, N. 

Nap. Kd. 1 (1862) 113-. 

, . Brioschi, F. G. Mt. 1 (1863) 26-. 

, . Lemonnier, H. [1874] Par. S. 

Mth. Bll. 3 (1875) 48-. 
, transformations. Kretkmvski, W. (xn) 

Krk. Ak. (Mt.-Prz.) Pam. 7 (1882) 69-. 
Quadratics, reduction to canonical form. Sardi, 

C. G. Mt. 5 (1867) 35-. 
Quadric automorphic linear transformation. 

Muir, T. [1897] Edinb. E. S. T. 39 (1900) 

209-. 
Quaternary quadratic form, automorphic linear 

transformations. Bachmann, . D. Nf. 

Tbl. (*1871) 138-. 
Eeal linear transformations whose invariant is 

an alternant. Taber, H. Am. Ac. P. 31 

(1896) 336-. 

. a real quadratic form. 
Taber, H. Am. Ac. P. 32 (1897) 75-. 

orthogonal substitution. Taber, H. Am. 
Ac. P. 28 (1893) 212-. 

Boots of substitutions. Kirkman, T. P. B. A. 
Ep. (1860) (pt. 2) 4-; (1861) (pt. 2) 4-. 

Solutions of the equation SX=XS. Voss, A. 
Munch. Ak. Sb. 26 (1897) 273-. 

Special automorphic groups and quadratic 
forms. Fricke, R. Mth. A. 39 (1891) 62-. 

Structure of linear groups with quadratic in- 
variants. Dickson, L. E. L. Mth. S. P. 
30 (1899) 70-. 

Substitutions permutable inter se. Cauchy, 
A, L. C. E. 21 (1845) 1188-. 

. , and other systems of substitutions. 

Cauchy, A. L. C. E. 21 (1845) 1238-. 

, product of two. Miller, G. A. Am. J. 

Mth. 22 (1900) 185-. 
, regular, irregular, and conjugate. Cauchy, 

A. L. C. E. 21 (1845) 835-, 895-, 931-, 

972-, 1025-. 

of six letters. Betti, E. C. E. 63 (1866) 
878. 

which do not alter value of a function. 
Cauchy, A. L. C. E. 21 (1845) 1234- . 

of several variables, 

number and form. Cauchy, A. L. C. E. 

21 (1845) 1287-. 
Ternary substitutions of determinant unity with 

integral coefficients. Burn-side, W. Mess. 

Mth. 24 (1895) 109-. 
Type of successive linear substitutions. Velt- 

mann, W. Arch. Mth. Ps. 58 (1876) 342-. 

2040 General theory of quantics. 

Absolute invariants of integral linear trans- 
formation groups. Hurwitz, A. Mth. A. 
20 (1882) 125-. 

Algebraic forms. Cambescure, E. Par. EC. 
Norm. A. 1 (1864) 269-. 

in any number of variables. Deruyts, J. 

Brux. Ac. Bll. 15 (1888) 951-. 

, geometrical applications. Le Paige, 
C. M. M. H. H. [1878] Brux. Mm. Cour. 
4 C , 42 (1879) (No. 4) 71 pp. 

with Hessian determinant vanishing 
identically. Noether, M. Erlang. Ps. Md. 
S. Sb. 8 (1876) 51-. 



Quantics 2040 

Algebraic forms with Hessian determinant 

vanishing identically. Gordan, P. , (& Noether, 

M. Mth. A. 10 (1876) 547-. 
, invariants of a class. Deruyts, J. Brux. 

Ac. Bll. 23 (1892) 152-. 
with p variables, theory of. Perrin, R. 

C. E. 104 (1887) 108-. 
, points in theory. Le Paige, C. M. M. 

H. H. Liege S. Sc. Mm. 9 (1882) (No. 4) 

23pp. 

, principle of classification. Rosanes, J. 
Crelle J. 76 (1873) 313-. 

, property. Le Paige, C. M. M. H. H. 

Mth. A. 15 (1879) 206- . 

with several series of variables. Le 
Paige, C. M. M. H. H. C. E. 94 (1882) 
31-, 69-. 

variables, development by polars. 

Capelli, A. Em. E. Ac. Line. Ed. 7 (1891) 
(Sem. 1) 161- ; 1 (1892) (Sem. 1) 3-. 

, symbolic representation. Clebsch, A. 
[1860] Berl. Mb. (1860) 536-; Crelle J. 59 
(1861) 1-. 

, theorem, with application to binary 
sextic. Ovidio, E. d'. Palermo Cir. Mt. 
Ed. 6 (1892) 225-. 

, theory. Sylvester, J. J. C. E. 101 

(1885) 1110-. 
, , arithmetical. Kronecker, L. Crelle 

J. Mth. 93 (1882) 365-. 
, , general. Capelli, A. Em. E. Ac. 

Line. Mm. 12 (1882) 529-. 
, , . Deruyts, J. Liege S. Sc. Mm. 

17 (1892) No. 4, vi + 157 pp. 
, , new. Sylvester, J. J. C. E. 101 

(1885) 1042-, 1225-, 1461. 
. , , operations in. Capelli, A. Mth. A. 

37 (1890) 1-. 

Anharmonic ratio and invariant theory of com- 
plex quantities. Schick, J. [1900] Munch. 

Ak. Sb. 30 (1901) 249-. 
Associated forms. Kohn, G. Wien Ak. Sb. 

100 (1891) (Ab. 2a) 865-. 
, general theory. Sylvester, J. J. Camb. 

and Dubl. Mth. J. 6 (1851) 289-. 

, theory of Clebsch and Gordan. Syl- 
vester, J. J. C. E. 86 (1878) 448-. 

Asyzygetic invariants, extension of a theorem. 

Sylvester, J. J. C. E. 102 (1886) 1430-. 
Boolian trinomial. Cockle, (Sir) J. [1868] 

Mess. Mth. 5 (1871) 33-. 
Canonical forms, a certain class. Roberts, R. A. 

[1894] N. Y. Am. Mth. S. Bll. 1 (1895) 

and hyperdeterminants, discovery in. 
Sylvester, J. J. Ph. Mg. 2 (1851) 391-. 

Chemico-algebraical theory. Frankland, E. 

Am. J. Mth. 1 (1878) 345-. 
Chemistry and algebra. Sylvester, J. J. Nt. 

17 (1878) 284. 
Combinants. Betti, E. Tortolini A. 1 (1858) 

344-. 
_. Gordan, P. [1871] Mth. A. 5 (1872) 

95-. 
, theory. Stroh, E. Mth. A. 22 (1883) 

393-. 
Contrariants, a new species of invariants. 

Sylvester, J. J. Ph. Mg. 18 (1884) 374-. 



142 



2040 



General Theory of Quantics 



Contravariants, invariants and covariants. 

Janni, G. G. Mt. 1 (1863) 174-, 194-, 240-, 

340-. 
Covariant, a definition. Keyser, C. J. N. Y. 

Am. Mth. S. Bll. 5 (1899) 468-. 

of system of n quantics. Newson, H. B. 
N. Y. Am. Mth. S. Bll. 2 (1896) 272-. 

Covariants. Cayley, A. [1852] Crelle J. 47 
(1854) 109-. 

. Jordan, C. C. E. 80 (1875) 875-. 

, algebra applied to theory. Roberts, M. 
[1861] QJ. Mth. 5 (1862) 18-. 

, composition, theorem. Jordan, C. C. E. 
81 (1875) 495-. 

, computation by transvection. McClintock, 
E. Am. J. Mth. 14 (1892) 222-. 

, etc. Bellavitis, G. Yen. At. (1858-59) 
65-, 82-. 

, formula for number of, extension to in- 
dependent linear transformations. Capelli, 
A. Em. E. Ac. Line. Mm. 15 (1883) 233-. 

of 4th order and 4th class of two conies, 
simultaneous. Bjorling, C. F. E. Stockh. 
Ofv. 33 (1876) No. 3, 21-. 

given degree, number of, for forms of 

any species. Capelli, A. G. Mt. 20 (1882) 

293-. 
, lists. McClintock, E. N. Y. Mth. S. Bll. 

1 (1892) 85-, 236. 
, note on certain. Le Paige, C. M. M. H. H. 

Brux. Ac. Bll. 1 (1881) 490-. 
, primary. Deruyts, J. Brux. Ac. Bll. 20 

(1890) 116-. 
, property of invariants of. Kohn, G. Wien 

Ak. Sb. 102 (1893) (Ab. 2o) 801-. 

of a system of quantics. Story, W. E. 
Mth. A. 41 (1893) 469-. 

.theorem. Cayley, A. Mth. A. 5 (1872) 625-. 
, . Jordan, C. C. E. 80 (1875) 1160-. 
_, _. Cayley, A. [1878] Crelle J. Mth. 87 

(1879) 82-. 

, , general. Faa de Bruno, F. C. E. 90 

(1880) 1203-. 

, theorems. Faa de Bruno, F. [1880] Crelle 

J. Mth. 90 (1881) 186-. 
, theory, etc. Brioschi, F. Mil. G. I. Lomb. 

8 (1856) 329-; Tortolini A. 1 (1858) 158-, 

296-, 549-; 2 (1859) 82-, 265-; 3 (I860) 

160-. 
Critical functions. Cockle, Jas. QJ. Mth. 4 

(1861) 97-, 265-. 
. Warren, J. W. [1863-64] QJ. Mth. 6 

(1864) 231-, 372-. 
Cubic forms with any number of variables, 

property. Voss, A. Mth. A. 27 (1886) 515-. 
Decomposable forms, especially cubics. Meyer, 

A. Ziir. Vjschr. 42 (1897) 149-. 
Decomposition of forms, conditions. Hada- 

mard, . Par. S. Mth. Bll. 27 (1899) 34-. 
Differences, products. Cayley, A. QJ. Mth. 

15 (1878) 174-. 
Differential equations satisfied by concomitants 

of quantics. Forsyth, A. R. L. Mth. S. P. 

19 (1889) 24-. 
Equation in S, applications of properties of 

quantics to. Brisse, C. N. A. Mth. 1 (1882) 

193-. 



2040 

Equivalence of forms. Jordan, C. C. E. 88 

(1879) 906- ; 90 (1880) 1422- ; Par. EC. Pol. 

J. 29 ( = eah. 48) (1880) 111-. 
Factorisable forms, theory. Rados, G. Mth. 

Termt. Ets. 4 (1886) 198-. 
Forms, calculus. Sylvester, J. J. Camb. and 

Dubl. Mth. J. 7 (1852) 52-, 179- ; 8 (1853) 

62-, 256-; 9 (1854)85-. 

of higher grade. Kronecker, L. Berl. Ak. 
Sb. (1883) 957-. 

, theorem. Voss, A. Munch. Ak. Sb. 18 

(1889) 15-. 
, theorems. Cazzaniga, T. G. Mt. 38 (1900) 

321-. 
Functions, 2nd order. Cayley, A. Crelle J. 

38 (1849) 105-. 
, similar, of several groups of functions or 

elements. Reiss, M. Quetelet Cor. Mth. 

5 (1829) 201-. 
Fundamental law, algebraic. Jacobi, C. G. J. 

Crelle J. 53 (1857) 275-. 

, , remarks on Jacobi' s paper. Bor- 
chardt, C. W. Crelle J. 53 (1857) 281-. 

Geometric significance of algebraic forms in 
theory of cubic curves. Gundelftnger, S. 
Mth. A. 3 (1875) 136-. 

Ground-forms and syzygants. (Extracts from 
:.) Hammond, J. ( 
(1883) 59, 84-, 150. 



J. H. Un. Cir. 



letters to Sylvester.) Hammond, J. (xn) 
. [2] ' 

theory. Gravelaar, N. L. W. A. 

N. Arch. Wisk. 3 (*1877) 193-. 
Higher algebra, note on a theorem. Dawson, 

H. G. Mess. Mth. 17 (1888) 69-. 
Homogeneity, principle, note. Serret, P. N. 

A. Mth. 14 (1855) 312-. 

Homogeneous isobaric functions, some pro- 
perties. Elliott, E. B. [1892] L. Mth. S. 

P. 24 (1893) 21-. 
Homology of sets. Cayley, A. QJ. Mth. 1 

(1857) 178. 
Hyperdeterminant calculus, exercises. Salmon, 

G. Camb. and Dubl. Mth. J. 9 (1854) 

19-. 

identity. Cayley, A. Mess. Mth. 21 (1892) 
131-. 

Hyperdeterminants. Cayley, A. [1846-51] 
Crelle J. 30 (1846) 1-; 34 (1847) 148- ; 
42 (1852) 368-. 

and canonical forms, discovery. Sylvester, 
J. J. Ph. Mg. 2 (1851) 391-. 

, conditional , scholium on theorem . Sylvester, 

J. J. Am. J. Mth. 1 (1878) 370-. 
Independent concomitants of simultaneous 

forms, number of. Sylvester, J. J. C. E. 

84 (1877) 1359-, 1427-. 
Inertia of quadratic form. Hermite, C. Crelle 

J. 53 (1857) 271-. 
. Borchardt, C. W. Crelle J. 53 

(1857) 281-. 
. Buchwald, E. (xn) Ts. Mth. 

2 (1872) 20-. 
forms, demonstration of law. Presle, 

de. Par. S. Mth. Bll. 15 (1887) 179-. 
, law. Frobenius, G. Berl. Ak. 

Sb. (1894) 241-, 407-. 
Invariant, definition. Elliott, E. B. Mess. 

Mth. 16 (1887) 5-. 



143 



2040 



General Theory of Quantics 



2040 



Invariant formation by operator Q. Note on 
Macmahon's theory. Sylvester, J. J. Mess. 
Mth. 13 (1884) 163-. 

functions associated with a transformable 
system. Deruyts, J. Brux. Ac. Bll. 32 
(1896) 82-. 

, law of formation. Deruyts, J. Brux. 

Mm. Cour. 4, 51 (1889) No. 10, 16 pp. 

, mutual differentiation. Deruyts, J. 
Brux. Ac. Bll. 16 (1888) 207-. 

, number. Deruyts, J. Brux. Ac. Bll. 

21 (1891) 437-. 
, property. Deruyts, J. Brux. Ac. Bll. 

26 (1893) 258-. 
, reduction. Deruyts, J. Brux. Ac. Bll. 

20 (1890) 265-; 24 (1892) 286-. 
, in the system of geometric variables. 

Deruyts, J. Brux. Ac. Bll. 24 (1892) 

558-. 

operations, a law of reciprocity. Capelli, A. 
Nap. Bd. 27 (1888) 189-. 

. which permit permutation. Capelli, A. 

Nap. Ed. 26 (1887) 236-; 27 (1888) 
45-. 

, permutative character. Capelli, A. 
Nap. Rd. 25 (1886) 135-. 

properties of system of a linear form and an 
alternate bilinear form. Morera, G. [1883] 
Tor. Ac. Sc. At. 18 (1882) 383-. 

sum of products of coefficients of pair of 
quantics. Eankine, W. J. M. QJ. Mth. 
1 (1857) 357-. 

systems, finite character. Maurer, L. 
Munch. Ak. Sb. 29 (1900) 147-. 

, general. Maurer, L. Miinch. Ak. Sb. 

18 (1889) 103-. 

theory. Meyer, F. D. Mth. Vr. Jbr. 1 
(1892) 79-. 

and chemistry, relation of formulae. 
Gordan, P., & Alexejeff, W. [1900] Erlang. 
Ps. Md. S. Sb. 32 (1901) 107-. 

Invariantive differential operators. Capelli, A. 

Nap. Ed. 26 (1887) 110-. 
Invariants. Brioschi, F. Tortolini A. 5 (1854) 

207-, 409-. 
. Bdlavitit, G. Yen. At. (1858-59) 65-, 

82-; Tortolini A. 2 (1859) 137-. 
. Blerzy, . N. A. Mth. 17 (1858) 301- ; 

18 (1859) 420-. 
. Sylvester, J. J. C. E. 85 (1877) 992-, 

1035-, 1091-. 

of algebraic forms, conception of. Study, E. 
Leip. Mth. Ps. B. 39 (1887) 137-. 

functions of forms. Wolffing, E. 
Mth. A. 43 (1893) 26-. 

, arithmetical. Poincare, H. As. Fr. C. E. 
(1881) 109-. 

calculus, test operators, properties; and 
application to development of any power of 
a logarithm. Sylvester, J. J. Ph. Mg. 32 
(1866) 461-. 

of a certain orthogonal transformation with 
reference to theory of strain and stress. 
Sharp, W. J. C. L. Mth. S. P. 13 (1881-82) 
216-. 

common to two quadratic forms in 2, 3, 
or 4 variables. Picquet, H. As. Fr. C. E. 
(1874) 1205-. 



Invariants, complete systems of. Hilbert, D. 

D. Mth. Vr. Jbr. 1 (1892) 61- ; Mth. A. 42 

(1893) 313-. 
, covariants, and contravariants. Foglini, G. 

Em. N. Line. At. 31 (1878) 249-. 
, , , theory. Janni, G. G. Mt. 2, 

(1864) 135-, 161-, 211-. 

and covariants as criteria for roots of an 
equation. Schramm, H. A. Mt. 1 (1867-68) 
259-; 3(1869-70)41-. 

, definition. Mansion, P. Brux. S. 

Sc. A. 12 (1888) (Pt. 1) 47-. 
of function transformed by a quadratic 

substitution. Spottiswoode, W. Em. E. Ac. 

Line. T. 7 (1883) 218-. 
system of three conies. Burnside* 

W. S. [1869] QJ. Mth. 10 (1870) 239-. 
, generation by integration. Hurwitz, A. 

Gott. Nr. (1897) 71-. 

of homogeneous forms. Mainardi, G, [1857} 
Mil. G. I. Lomb. 9 (1856) 208-. 

, identical equation in theory. Cayley, A* 
QJ. Mth. 12 (1873) 115-. 

of integral polynomials, certain. Laisant* 
C. A. Palermo Cir. Mt. Ed. 8 (1894) 
249-. 

, principles deduced from theory of linear 
formations. Gram, J. P. (vn) [1873] Mth. 
A. 7 (1874) 230-. 

of quadratic forms. Kleiber, J. Z. Mth. 
Ps. 37 (1892) 79-. 

and higher geometry. Study, E* 

Leip. Mth. Ps. B. 49 (1897) 443-. 

quantics. Deruyts, J. Brux. Mm. Cour. 

4, 52 (1890-93) No. 2, 28 pp. 

in special mathematics. Campoux, P. de. 
N. A. Mth. 8 (1869) 395-; 9 (1870) 113-. 

, theorem, fundamental. Ovidio, E. d'. G. 

Mt. 15 (1877) 187-. 
, , , proof. Christoffel, E. B. [1867] 

Crelle J. 68 (1868) 246-. 
, , , . Aronhold, . Crelle J. 69 

(1868) 185-. 
, of Hilbert. Gordan, P. Mth. A. 42 

(1893) 132-. 
, , proof. Dahl, C. Ts. Mth. 4 U880V 

154-. 
, theory. Spottiswoode, W. E. S. P. 7 

(1854-55) 204-. 
, . Combescure, E. Liouv. J. Mth. 20 

(1855) 337-. 
, . Faa de Bruno, F. Tortolini A. 6 

(1855) 328-. 
, . Aronhold, S. H. Crelle J. 62 (1863} 

281-. 
, . Cayley, A. [1870] Mth. A. 3 (1871V 

268-. 
, . Christoffel, E. B. [1881] Mth. A. 19 

(1882) 280-. 
_ _. Veltmann, . Z. Mth. Ps. 34 (1889) 

321-. 
, . Maurer, L. Crelle J. Mth. 107 (1891V 

89-. 
, . Hilbert, D. Gott. Nr. (1891) 232-; 

(1892) 6-, 439-. 

_, _. Weber, H. Gott. Nr. (1893) 109-. 
, . Hurwitz, A. Mth. A. 45 (1894) 

381-. 



144 



2040 



General Theory of Quantics 



2040 



Invariants, theory, elementary development of 

principles. Gram, J. P. (xii) Ts. Mth. 3 

(1873) 1-. 
, , foundations. Veltmann, W. Z. Mth. 

Ps. 22 (1877) 277-. 
, , fundamental problem. Clebsch, R. F. A . 

Gott. Ab. 17 (1872) 62 pp. ; Mth. A. 5 (1872) 

427-. 
, , new application. Fuchs, L. Crelle J. 

Mth. 81 (1876) 97-. 
Involution, theory. Cayley, A. [1864] Camb. 

Ph. S. T. 11 (1871) 21-. 
, , in connection with algebraic forms. 

Deruyts, F. Brux. Ac. Bll. 14 (1887) 

650-. 
Involutions. Gerbaldi, F. Palermo Cir. Mt. 

Ed. 9 (1895) 167-. 

with ordinary singularities. Guccia, G. B. 
Palermo Cir. Mt. Ed. 7 (1893) 49-; 8 (1894) 
227-. 

Irrational covariants. Klein, F. Gott. Nr. 

(1888) 191-. 
Isobaric function, properties. Amanzio, D. 

Nap. Ac. Pont. At. 17 (1887) 85-. 
functions. Fan de Bruno, F. Tortolini A. 

7 (1856) 76-. 

. Stassano, P. G. Mt. 24 (1886) 
57-. 

homogeneous functions. Cesaro, E. G. Mt. 
22 (1884) 33-, 166. 

Jacobians and polar opposites. Clifford, W. K. 

(i) Mess. Mth. 2 (1864) 229-. 
Joachimsthal, theorem, remark. Lebesgue, 

V. A. N. A. Mth. 7 (1848) 225-. 
Kronecker's modular systems, and inertia of 

quadratic forms. Netto, E. Crelle J. Mth. 

110 (1892) 184-. 
Linear forms, theory. Hensel, K. Crelle J. 

Mth. 107 (1891) 241-. 
transformations and theory of covariants. 

Deruyts, J. Brux. Mm. Cour. 4, 51 (1889) 

No. 9, 22 pp. 
Multiple forms, theorem. Peano, G. Tor. Ac. 

So. At. 17 (1881) 73-. 
involutions. Valyi, G. Mth. Termt. Ets. 

12 (1894) 394-; 13 (1895) 408- ; 14 (1896) 

381- ; Mth. Nt. B. Ung. 13 (1897) 244-, 

259-, 343-. 
points in systems of equations and of their 

Jacobian. Barcroft, D. [1886] J. H. Un. 

Cir. [6] (1886-87)' 30. 
Multiplicity, new theory. Sylvester, J. J. Ph. 

Mg. 3 (1852) 460-. 
Operator that produces all the covariants and 

invariants of any system of quantics. Story, 

W. E. L. Mth. S. P. 23 (1892) 265-. 
Perpetuants, applications to theory of finite 

quantics. Hammond, J. Am. J. Mth. 8 

(1886) 104-. 
Projective invariants, report. White, H. S. 

[1898] N. Y. Am. Mth. S. Bll. 5 (1899) 

161-. 
Quadratic forms, formulae. Day, E. H. G. 

QJ. Mth. 14 (1877) 184-. 
, geometric interpretation of invariants. 

Hesse, L. 0. Crelle J. 45 (1853) 82-. 
, non-homogeneous. Cremona, L. Mil. 

I. Lomb. Ed. 4 (1867) 199-. 



Quadratic forms, physical theories involving. 
Maxwell, J. C. L. Mth. S. P. 4 (1871-73) 
334-. 

in n variables. Cotterill, J. H. (n) 
Mess. Mth. 2 (1864) 210-. 

, reduction. Jordan, C. C. E. 93 (1881) 
113-, 181-, 234-. 

, theorem, and application to small oscil- 
lations. Weierstrass, C. T. W. Berl. Mb. 
(1858) 207- ; Berl. Ak. Mb. (1879) 430-. 

, of Weierstrass. Brioschi, F. (vi 

Adds.) Tortolini A. 1 (1858) 250-. 

Quadrilinear forms. Le Paige, C. M. M. H. H. 
[1882] Tor. Ac. Sc. At. 17 (1881) 299-. 

Quadriquadric function, two invariants of a. 
Cayley, A. Mess. Mth. 20 (1891) 68-. 

Quantic. Catalan, E. C. C. E. 47 (1858) 
1073-. 

with n variables, reduction to one with n - 1. 
Hesse, L. O. Crelle J. 42 (1851) 117-. 

Quantics. Lejeune-Dirichlet, G. Berl. B. (1841) 

280-. 

. Genoechi, A. N. A. Mth. 12 (1853) 393-. 
. Cayley, A. Phil. Trans. 144 (1854) 245-; 

146 (1856) 101-, 627-; 148 (1859) 415-, 429-; 

149 (1860) 61-; 151 (1862) 277-; 157 (1867) 

513- ; 161 (1871) 17-; 169 (1878) 603- ; E. 

S. P. 23 (1875) 496 (corr.). 
. Laisant, . Par. S. Mth. Bll. 20 (1892) 

117-. 

of alternate numbers used for determining 
invariants and covariants of quantics in 
general. Clifford, W. K. L. Mth. S. P. 
10 (1878-79) 124-. 

, decomposition into linear factors. Painvin, 

L. C. E. 50 (1860) 84-; Liouv. J. Mth. 6 

(1861) 209-. 
, general properties. Sylvester, J. J. Camb. 

and Dubl. Mth. J. 6 (1851) 1-. 
, theorems. Gundelfinger, S. Mth. A. 

4 (1871) 164-. 

, theory and application to curves and 
surfaces. Reiss, M. Mth. A. 2 (1870) 

385-. 
, index symbol. Carmicliael, E. Camb. and 

Dubl. Mth. J. 6 (1851) 277-; 8 (1853) 

81-. 
, method. Terquem, 0. N. A. Mth. 7 (1848) 

5-. 
, note. Aelt, . N. A. Mth. 3 (1864) 

289-. 
, properties. Malmsten, C. J. Ts. Mt. Fys. 

4 (1871) 225-. 
, property. Gukovskij, A. N. Es. S. Nt. 

Mm. (Mth.) 11 (1890) 145-. 
, theory. Hesse, L. O. Crelle J. 56 (1859) 

263-. 
Eeciprocity, Hermite's law. Gordan, P. Gott. 

Nr. (1897) 182-. 
, , extension. Deruyts, J. Brux. Ac. 

Bll. 22 (1891) 11-. 

laws. Igel, B. Wien Ak. D. 54 (1888) 
(Ab. 2) 75-. 

in theory of algebraic forms. Brioschi, F. 
Tortolini A. 7 (1856) 303-. 

Eeduced invariant functions, characteristic 
equations. Deruyts, J. Brux. Ac. Bll. 25 
(1893) 450-. 



145 



2050 Quantics 

Eeducibility of every quadratic form to sum of 

n squares. Sylvester, J. J. (vi Adds.) Ph. 

Mg. 4 (1852) 138-. 
Representation of definite forms as sums of 

squares. Hilbert, D. Mth. A. 32 (1888) 342-. 
Reproduction of forms. Poincare, H. C. R. 

97 (1883) 949-. 
Resolution into linear factors. Walker, J. J. 

QJ. Mth. 6 (1864) 328-. 
of a form of mth order and nth 

degree. Schendel, L. Z. Mth. Ps. 32 (1887) 

83-. 
Roots of solvable quantics as symmetric 

functions of homologues. Kummell, C. H. 

Am. J. Mth. 18 (1896) 74-. 
Secondary invariants. Rogers, L. J. L. Mth. 

S. P. 20 (1889) 161-. 
Semi-combinants as concomitants of affiliants. 

White, H. S. Am. J. Mth. 17 (1895) 235-. 
Seminvariants. Petr, K. Prag Cesk6 Ak. Fr. 

Jos. Rz. (Tftda 2) 6 (1897) Art. 38, 22 pp.; 

Fschr. Mth. (1897) 108. 
, generalisation. Deruyts, J. Brux. Mm. 

Cour. 4, 51 (1889) No. 8, 20 pp. 
Symbolic invariants in general theory of 

algebraic forms, relations. Pascal, E. Rm. 

R. Ac. Line. Mm. 5 (1888) 375-. 
Systems, finite, of forms in theory of rational 

functions. Kdnig, J. [1880?] Mth. A. 18 

(1881) 69-. 
Syzygetic relations among powers of linear 

quantics. Clifford, W. K. [1869] L. Mth. 

S. P. 3 (1869-71) 9-. 
, Clifford's paper. Cayley, 

A. [1891] L. Mth. S. P. 23 (1892) 99-. 
Syzygies. Cayley, A. (xn) J. H. Un. Cir. 

[2] (1883) 150. 
, irreducible, of quantics, tables. Sylvester, 

J. J. Am. J. Mth. 4 (1881) 41-. 
among perpetuants, expression by means of 

n"tions. MacMahon, (Capt.) P. A. Am. 
th. 10 (1888) 149-. 

Transformation principle of Clebsch, and appli- 
cation. Gundelfinger, S. [1872] Mth. A. 6 
(1873) 16-. 

Trilinear forms. Le Paige, C. M. M. H. H. 
[1881] C. R. 92 (1881) 1048-, 1103- ; 93 

(1881) 264-, 509- ; Rm. N. Line. At. 35 

(1882) 140-. 

, a system of two. Le Paige, C. M. M. 

H. H. Rm. N. Line. At. 35 (1882) 54-. 
Universal invariants. Eabut, . C. R. 115 

(1892) 926-, 1028. 
Variables of different kinds, forms in several 

series. Deruyts, J. Brux. Ac. fill. 28 (1894) 

157-. 

2050 Binary Forms. 

Absolute invariant and covariants of a bi- 
quadratic form, geometrical representation. 
Lacour, . N. A. Mth. 17 (1898) 341-. 

Algebraic forms, theorem, with application to 
binary sextic. Ovidio, E. d'. Palermo Cir. 
Mt. Rd. 6 (1892) 225-. 

Anharmonic ratio and absolute invariant of 
biquadratic. Wedekind, L. Mth. A. 17 
(1880) 1-. 



Binary Forms 2050 

Apolarity, applications of principle. Igel, B. 

Wien Ak. Sb. 92 (18861 (Ab. 2) 1153-. 
Asyzygetic covariants of the third degree of a 

binary form. Stroh, E. Mth. A. 31 (1888) 

444-. 

Binary cubic form, automorphic transforma- 
tion. Cayley, A. L. Mth. S. P. 14 (1883) 

103-. 
, geometrical representation. Ger- 

baldi, . Palermo Cir. Mt. Rd. 3 (1889) 

276-. 
, relations between roots and those of 

first covariants. Mainardi, G. Rm. At. N. 

Line. 26 (1873) 391-. 
forms. Eisenstein, G. Crelle J. 27 

(1844) 89*. 
. Arndt, F. Grunert Arch. 17 (1851) 

1- ; Crelle J. 53 (1857) 309-. 
. Hermite, C. QJ. Mth. 1 (1857) 

20-. 
. Cayley, A., d- Hermite, . QJ. 

Mth. 1 (1857) 85-. 
. Battaglini, G. Nap. Rd. 3 (1864) 

109-, 163-. 
. Hermite, C. Crelle J. 63 (1864) 

30-. 
. Beltrami, E. Bologna Ac. Sc. Mm. 



. Brioschi, F. [1876] Mth. A. 11 

(1877) 111-. 
. Tannery, J. Bll. Sc. Mth. As. 1 

(1877) (Pt. 1) 260-. 
. Pepin, T. Rm. N. Line. At. 37 

(1884) 227-. 
, classification. Pepin, T. Rm. N. 

Line. At. 39 (1886) 23-. 

, complete form-system for three. 
Gall, (Frhr.) von. Mth. A. 45 (1894) 
207-. 

, geometrical application. Torelli, G. 

G. Mt. 24 (1886) 270-. 
, interpretation. Retail, V. Palermo 

Cir. Mt. Rd. 2 (1888) 25-. 
, representation of system of two, 

and their associated forms. Roberts, W. R. W. 

[1881] L. Mth. S. P. 13 (1881-82) 16-. 
, imaginary elements. Pittarelli, G. 

G. Mt. 23 (1885) 368-. 
, reduction. Hermite, C. C. R. 48 

(1859) 351-. 
, simultaneous. Clebsch, R. F. A. 

Crelle J. 67 (1867) 360-. 
, system of two. Gundelfinger, S. 

Mth. A. 7 (1874) 452-. 
, . Gerbaldi, F. G. Mt. 

17 (1879) 373-. 
, three. Igel, B. Wien Ak. 

D. 49 (1885) (Ab. 2) 277-. 
, system of two. Caporali, E. Nap. 

Rd. 22 (1883) 95-. 
, . Mollo, C. G. Mt. 28 

(1890) 330-. 
, several. Torelli, G. Nap. Rd. 

24 (1885) 258-. 

, geometrical representation. Gerbaldi, 
. Palermo Cir. Mt. Rd. 3 (1889) 276-. 

and quartic forms, geometry. Newson, 

H. B. [1893] Kan. Un. Q. 2 (1894) 85-. 



146 



2050 Binary Forms 

Binary cubics, geometric interpretation. Re- B 
tali, V. [1887] Palermo Cir. Mt. Ed. 2 
(1888) 25-. 

decimic, reduction to canonical form. 
Spottiswoode, W. B. A. Ep. (1861) (pt. 2) 

11 . 

evectant form. Roberts, S. QJ. Mth. 11 

(1871) 42-. 

expressions, canonical form. Lerch, M. 
Prag Sb. (1883) (Mth. Vortr.) 447-. 

form, determination from initial members 
of covariants. Gordan, P. Mth. A. 40 
(1892) 503-. 

of 7(th order with a sum of powers n e . 
Paolis, R. de. Em. E. Ac. Line. Mm. 12 
(1882) 405-. 

, conditions for factor of mth 

order. Igel, B. [1880] Wien Ak. Sb. 82 
(1881) (Ab. 2) 943-. 

forms. Betti, E. Tortolini A. 7 (1856) 60-. 
. Brioschi, F. Tortolini A. 7 (1856) - 

231-. 
. Gundelfinger, S. [1871] Crelle J. 74 - 

(1872) 87-. 

. Cassani, P. G. Mt. 10 (1872) 230-. 

. Motto, C. G. Mt. 27 (1889) 327-. 

, absolute invariants, partial differential 

equations satisfying, in higher transforma- 
tions. Clebsch, R. F. A. Gott. Ab. 15 (1870) 
(Mth.) 65-. 

of alternate variables. Clifford, W. K. 

L. Mth. S. P. 10 (1878-79) 214-. 

, any degree. Battaglini, G. [1866] Nap. 

At. Ac. Sc. 3 (1866-68) (No. 10) 34 pp. 

, application to differential equation. 
Battaglini, G. G. Mt. 24 (1886) 128-. 

, plane geometry. Laguerre, E. 
C. E. 78 (1874) 744-. 

, canonical form. Cayley, A. Crelle J. 

54 (1857) 48-. 

, , new, of groups of. Meyer, F. W. 

Mth. A. 21 (1883) 434-. 

, class. Klein, [C.] F. [1874] (vm) Er- 
lang. Sb. Ps. Md. S. 6 (1874) 160- ; (x) 7 
(1875) 49-. 

, . Brioschi, F. [1876] A. Mt. 8 (1877) 

24-. 

, , properties. Brioschi, F. Em. E. 
Ac. Line. Ed. 2 (1886) (Sem. 1) 302-. 

, classes, two. Maisano, G. Em. E. Ac. 

Line. Mm. 15 (1883) 44-. 
, Clebsch's theory, two points in. Ovidio, 

E. d'. Tor. Ac. Sc. At. 22 (1886-87) 427-. 

, combined, invariants. Bessel, A. St. 
Pet. Ac. Sc. Mm. (Rs.) 14 (1868) (Suppl.) ' 
No. 3, 88 pp. 

, common factor of two. Noether, M. 
Erlang. Ps. Md. S. Sb. 27 (1896) 110-. 

, , Noether's paper. Liiroth, J. 

Erlang. Ps. Md. S. Sb. 27 (1896) 119. 
, construction. Thieme, H. Mth. A. 23 

(1884) 597-. 
and correlations in n dimension space. 

Waelsch, E. Mh. Mth. Ps. 6 (1895) 261-, 

375-. 

forms and elimination. Steplianos, C. 
Par. EC. Norm. A. 1 (1884) 329-. 

147 



Binary Forms 2050 

inary forms of equal degree, systems of, and 
complete system of cubics. Peano, G. Tor. 
Ac. Sc. At. 17 (1881) 580-. 
and equation of 6th degree. Brill, A. 
Mth. A. 20 (1882) 330-. 

- , 1st four degrees. Battaglini, G. G. 
Mt. 2 (1864) 170-, 193-, 243-, 340 ; 3 (1865) 
24-, 51-, 218-. 

- , pertaining to a ternary quad- 
ratic form. Battaglini, G. Nap. Ed. 4 (1865) 
351- ; 5 (1866) 35-, 141-. 

, and 2nd degrees. Battaglini, G. Nap. 
Ed. 3 (1864) 76-. 

- , 3rd and 4th degrees. Bessel, A. A. 
(xn) Eec. Mth. (Moscou) 3 (1868) (Pt. 1) 
123-. 

, geometric interpretation. Wedekind, L. 

Mth. A. 9 (1876) 209-. 

- , . Lindemann, F. Mth. A. 23 

(1884) 111-. 

- with integral coefficients, reduction. 
Hermite, C. Crelle J. 36 (1848) 357-. 

linear automorphic transformations. 

Klein, C. F. [1875] Mth. A. 9 (1876) 183-. 

- , mixed, 3rd and 4th degrees. Battaglini, 
G. Nap. Ed. 3 (1864) 282-. 

- , mutual transformation, possibility of. 
Clebsch, R. F. A. [1869] Mth. A. 2 (1870) 
373-. 

- with prescribed discriminant. Hilbert, D. 
Mth. A. 31 (1888) 482-. 

- i . functional determinant. Hilbert, 

D. Mth. A. 33 (1889) 227-. 

- , representation. Clebsch, R. F. A., & 
Gordan, P. [1867] A. Mt. 1 (1867-68) 23-. 

, , application to hyperelliptic integrals. 

Gordan, P. A. Mt. 2 (1868-69) 346-. 

- , in plane and space. Laguerre, E. 
(x) Par. S. Phlm. Bll. 8 (1872) 83-. 

, as sums of powers. Rosanes, J. [1872] 

Crelle J. 75 (1873) 172-. 
, , especially 2n-ic by n + 1 

powers. Bauer, G. Munch. Ak. Sb. 22 

(1893) 3-. 

- represented on curve of genus zero. 
Maisano, G. Palermo Cir. Mt. Ed. 1 (1887) 
14-. 

with several series of variables. Le Paige, 

C. M. M. H. H. Brux. Ac. Bll. 2 (1881) 40-; 
Lisb. J. Sc. Mth. 9 (1883) 211-. 

, simultaneous, system of four. Perrin, R. 

Par. S. Mth. Bll. 15 (1887) 45-. 

, some. Brioschi, F. [1876] Erlang. Ps. 

Md. S. Sb. 9 (1877) 30-. 
_ t system derivable from a single form. 
Astis, F de. G. Mt. 36 (1898) 161-. 
_ , systems, simultaneous. Gordan, P. 
Mth. A. 2 (1870) 227-. 

, theorem. Arcais, F. d'. Bologna Ac, 

Sc. Mm. 9 (1878) 173-. 

, _. Qcagne, M. d'. C. E. 102 (1886) 

916-. 

- , and application to biquadratic. 
Arndt, F. Grunert Arch. 17 (1851) 409-. 

, of Hilbert's. Brioschi, F. Palermo 

Cir. Mt. Ed. 10 (1896) 153-. 

- , , and Jacobian. Faa de Bruno, F. 
Mth. A. 18 (1881) 280-. 

E2 



2050 Binary Forms 

Binary forms, theorem on fnth differentials. 

Dawson, H. G. Mess. Mth. 18 (1889) 145- . 
, theorems, and application to multiple 

roots of sextic equation. Maisano, G. Km. 

B. Ac. Line. T. 7 (1883) 231-. 
, , extensions. Ovidio, E. d\ Tor. Ac. 

Sc. At. 14 (1878) 963-. 
, theory. Hermite, C. Camb. and Dubl. 

Mth. J. 9 (1854) 172-. 
, . Clebsch, R.F. A. Gott. Nr. (1870) 

405-. 
, . Noether, M. Erlang. Ps. Md. S. 

Sb. 13 (1881) 41-. 
, . Gundelfinger, S. Gott. Nr. (1883) 

115- ; Crelle J. Mth. 100 (1887) 413-. 
, . Deruyts, J. Brux. Ac. Bll. 14 

(1887) 53-. 
, . Waelsch, E. Wien Ak. Sb. 100 

(1891) (Ab. 2o) 574-. 
, , notes. Pittarelli, G. G. Mt. 15 

(1877) 362-. 

, _, point in. Capelli, A. G. Mt. 16 

(1878) 217-. 

, transformations/ geometric interpreta- 
tion. Clebsch, R.F. A. Gott. Nr. (1871) 335-. 

with two series of variables, new symbol 

in theory. Pascal, E. Nap. Bd. 26 (1887) 
200-. 

vanishing covariants. Gordan, P. 
Mth. A. 12 (1877) 147-. 

which are complete powers, conditions 

for. Hilbert, D. Mth. A. 27 (1886) 158-. 
polars of a form. Wiederhold, P. 

Mth. A. 8 (1875) 444-. 
whose variables are fundamental integrals 

of a linear differential equation. Vernier, P. 

Par. S. Mth. Bll. 22 (1894) 133-. 

groups with special property of combinants. 
Hilbert, D. Mth. A. 30 (1887) 561-. 

nonic, complete system of groundforms. 
Sylvester, J. J. Am. J. Mth. 2 (1879) 98-. 

octavic, complete system of forms. Gall, 
(Frhr.) von. Mth. A. 17 (1880) 31-, 139-, 
456. 

, proof of impossibility of its possessing 

groundform of deg.-order 10 . 4. Sylvester, 
J. J. Am. J. Mth. 4 (1881) 62-. 

, properties. Brioschi, F. C. B. 96 (1883) 

1689-. 

quadratic forms, system of three. Astis, F. 
de. G. Mt. 37 (1899) 148-. 

quantic, a, b, c form. Hammond, J. L. Mth. 
S. P. 27 (1896) 393-. 

quantics. Brioschi, F. Tortolini A. 7 (1856) 
5-, 15-, 69-. 

, derivatives. Cayley, A. QJ. Mth. 15 

(1878) 157-. 

, reduction to canonical form. Faa de 
Bruno, F. Liouv. J. Mth. 17 (1852) 193-. 

quartic form, Legendre's reduction to canoni- 
cal form. Warren J. [1865] QJ. Mth. 7 
(1866) 338-. 

, properties of a. Brioschi, F. G. Mt. 

22 (1884) 130-. 

, theory. Igel, B. Mh. Mth. Ps. 10 

(1899) 102-. 

forms. Arndt, F. Grunert Arch. 18 

(1852) 111-. 



Binary Forms 2050 

Binary quartic forms. Battaglini, G. Nap. 

Bd. 3 (1864) 201-, 234-. 
. Clebsch, R. F. A. Crelle J. 67 

(1867) 371-. 

and elliptic functions, connection 
between. Study, E. Am. J. Mth. 17 (1895) 
216-. 

in involution. Battaglini, G. Nap. 

Bd. 3 (1864) 263-. 
, simultaneous system of two. Bertini, 

E. [1875] G. Mt. 14 (1876) 1-. 
, system derivable from same quintic. 

Stasi, F. G. Mt. 37 (1899) 160-. 
and ternary cubics. Brioschi, F. [1875J 

A. Mt. 7 (1876) 52-. 

quintic. Battaglini, G. Bm. B. Ac. Line. 
At. 2 (1875) 582-. 

, application of theorem to. Ovidio, E. d\ 

Palermo Cir. Mt. Bd. 7 (1893) 1-. 

, canonical form. MacMahon, P. A* 
QJ. Mth. 19 (1883) 337-. 

and sextic, new canonical forms. Groice t 

B. E. Kan. Un. Q. 6 (1897) 201-. 

quintics. Ovidio, E. d'. Tor. Ac. Sc. At. 
15 (1879) 591-. 

. Maisano, G. Bm. B. Ac. Line. Mm. 

14 (1883) 97-. 

septic. Sylvester, J. J. C. B. 87 (1878) 
899-. 

, complete form-system of the. Gall> 
(Frhr.) von. Mth. A. 31 (1888) 
318-. 

sextic. Perrin, R. C. E. 96 (1883) 1717-, 
1776-, 1842-. 

. Maisano, G. Em. B. Ac. Line. Mm. 

19 (1884) 9-. 

, formulae relative to. Ovidio, E. d\ 
Tor. Ac. Sc. At. 27 (1892) 535-; 28 (1893) 
133. 

, its syzygies and their relations. Ham- 
mond, J. Am. J. Mth. 7 (1885) 327-. 

sextics. Clebsch, R. F. A., & Gordan, P. 

C. B. 64 (1867) 582-. 

. Clebsch, R.F. A. Gott. Ab. 14 (1869) 

75pp. 

. Bolza, 0. Mth. A. 30 (1887) 546-. 

-with linear transformations into them- 
selves. Bolza, 0. Am. J. Mth. 10 (1888) 

47-. 
Canonic roots of binary quantic of odd order. 

Cayley, A. Ph. Mg. 25 (1863) 206-. 
, sequel to Cayley's theorems. Sylvester^ 

J. J. Ph. Mg. 25 (1863) 453-. 
Canonical forms, point in Sylvester's theory. 

Morley, F. [1900] N. Y. Am. Mth. S. Bll. 7 

(1901) 202, 206. 
Catalecticant is an invariant, proof. Humbert, 

. As. Fr. C. B. (1888) (Pt. 2) 163-. 
Combinants of algebraic binary forms. Le 

Paige, C. M. M. H. H. Brux. Ac. Bll. 48 

(1879) 530-. 
binary associated with curves of 4th 

order. Berzolari, L. A. Mt. 20 (1892-93) 

101-. 
form-systems, etc. Gross, W. Mth. A. 

32 (1888) 136-. 
linear system of quintics. Berzolari, L^ 

Palermo Cir. Mt. Ed. 7 (1893) 5-. 



148 



2050 Binary Forms 

Combinants of two binary biquadratic forms, 

complete system. Stephanos, C. C. E. 97 

(1883) 27-. 
- forms, complete system. Stroh, E. 

Mth. A. 34 (1889) 321-. 
Concomitant binary forms in terms of the roots. 

MacKinnon, (Miss) A. L. A. Mth. 9 (1894- 

95) 95- ; 12 (1898-99) 95-. 
Concomitants, irreducible, of any number of 

binary quartics. Young, A. L. Mth. S. P. 

30 (1899) 290- . 
Condition for involution of two quartics. 



Binary Forms 2050 

Covariants, elementary, of system of two bi- 
quadratic binary forms, number. Sylvester, 
J. J. C. B. 84 (1877) 1285-. 

, fundamental, of binary cubo-quadratic 
system. Sylvester, J. J. C. E. 87 (1878) 
242-, 287-. 

, , system of 2 cubics, true number. 
Sylvester, J. J. C. E. 89 (1879) 828-. 

, independent, of binary forms, number. 
Stroh, E. Mth. A. 31 (1888) 441-. 

and invariants of binary form, theorem. 
Gordan, P. Crelle J. 69 (1868) 323-. 



Alagna, E. Palermo Cir. Mt. Ed. 5 (1891) . Brioschi, F. Tortolini A. 1 

301-. (1858) 296-, 549-; 2 (1859) 82-, 265-; 3- 

Conditions that binary octavic should have (I860) 160-. 

4 double points. Alagna, R. Palermo Cir. . Bonsdor/, E. [E. J.] [1876] 

Mt. Ed. 4 (1890) 25-. Helsingf. Acta 11 (1880) 167-. 

form F(x 2 , y-) maybe expressed in terms , relations. Perrin, E. C. E. 

of an exact square. Giordano, G. G. Mt. 96 (1883) 426-. 

, residues. Perrin, R. Par. 



37 (1899) 367-. 
Conjugate binary forms and their geometric 

construction. Schlesinger, 0. [1882] Mth. 

A. 22 (1883) 520-. 
Covariant formula. Caijley, A. QJ. Mth. 16 

(1879) 224-. 

Covariants of binary cubic, geometrical inter- 
pretation. Cayley, A. QJ. Mth. 10 (1870) 

148-. 
forms. Cayley, A. Crelle J. 50 (1855) 

277-. 
. Betti, -E. Tortolini A. 1 (1858) 

129-. 
. Jordan, C. C. E. 82 (1876) 269- ; 

87 (1878) 202- ; Liouv. J. Mth. 2 (1876) 177- ; 

5 (1879) 345-. 
. Le Paige, C. M. M. H. H. Brux. 

Ac. Bll. 49 (1880) 113-. 
. Petersen, J. P. C. (xn) Ts. 

Mth. 4 (1880) 177- ; 5 (1881) 33- ; 6 (1889) 

152- ; Fschr. Mth. (1888) 117-. 
, development. Bonsdorff, E. 

[E. J.] [1877] St. Pet. Ac. Sc. Bll. 24 (1878) 



, geometric representation. Linde- 

mann, C. L. F. Par. S. Mth. Bll. 5 (1877) 

113- ; 6 (1878) 195-. 
, reduction of two. Stroh, E. Mth. 

A. 22 (1883) 290-. 
quantic. Cayley, A. B. A. Ep. 41 

(1871) (Sect.) 9-. 

, finite number of. Cayley, A. 
QJ. Mth. 17 (1881) 137- ; Mth. A. 34 (1889) 
319-. 

of rith degree. Roberts, M. QJ. 

Mth. 4 (1861) 168-, 324- ; 5 (1862) 

quintic. Roberts, M. Tortolini A. 3 

(1860) 340-. 
, biquadratic (Cayley's formula). Brioschi, F. 

Crelle J. 53 (1857) 377-. 

of a biquadratic form, geometrical repre- 
sentation. Le Paige, C. M. M. H. H. Brux. 
Ac. Bll. 50 (1880) 115-. 

cubo-biquadratic system. Le Paige, 
C. M. M. H. H. Brux. Ac. Bll. 46 (1878) 
765-. 

, double, of binary forms. Laguerre, E. (x) 
Par. S. Phlm. Bll. 8 (1872) 48-. 



S. Mth. Bll. 11 (1883) 88-. 

, theory. Dienger, J. [1870] 

Prag Ab. 4 (1871) 47 pp. 

even character of binary sextic 

relations. Stephanos, C. C. E. 96 (1883) 
232-, 1564-. 

same binary form, relations be- 
tween. Brioschi, F. A. Mt. 11 (1882-83) 291-. 

, irrational, of certain binary forms. Study, E. 
Am. J. Mth. 17 (1895) 185-. 

, irreducible, of binary octavic. Sylvester, 
J. J. C. E. 93 (1881) 192-, 365-. 

, , septic. Sylvester, J. J. C. E. 87 
(1878) 505-. 

, , cubo-biquadratic binary system, 
exact number. Sylvester, J. J. C. E. 87 

(1878) 477-. 

, linear fundamental, of two binary cubics. 

Ovidio, E. d'. Tor. Ac. Sc. At. 15 (1879) 

267-. 
, simultaneous, of two quartics and of two 

quintics. Pascal, E. A. Mt. 16 (1888-89) 

85-. 
, special mode of forming. Wiltheiss, E. 

Mth. A. 35 (1890) 433-; 36 (1890) 134- ; 37 

(1890) 229-. 

of system of three binary forms, principle 
for obtaining. Igel, B. [1882] Wien Ak. D. 
46(1883) (^6.2)350-. 

, two simultaneous, of two biquadratic binary 
forms. Ovidio, E. d\ Tor. Ac. Sc. At. 15 

(1879) 301-. 

Cubi-quadric system. Hammond, J. Am. J. 

Mth. 8 (1886) 138-. 
Cubic resolvent of a binary quartic. White, 

H. S. N. Y. Am. Mth. S. Bll. 3 (1897) 250-. 

transformation of a binary cubic form. 
Torelli, G. Nap. Ac. Pont. At. 18 (1888) 
215-. 

Determinant, functional, of any number of 
binary forms. Le Paige, C. M. M. H. H. 
C. E. 92 (1881) 688-. 

Differential operators, certain linear, inter- 
change of variables in. Elliott, E. B. [1889] 
Phil. Trans. (A) 181 (1891) 19-. 

Discriminant of binary cubic, arithmetical 
theorem connected with. Sylvester, J. J. 
C. E. 60 (1865) 1011-, 1121-. 



149 



2050 Binary Forms 



Binary Forms 2050 



Discriminant of binary cubic, theorem. Eisen- 

stein, G. Crelle J. 27 (1844) 105-. 
quantic. Cay ley, A. QJ. Mth. 10 

(1870) 23. 
, calculation. Bauer, G. Munch. 

Ak. Sb. 16 (1887) 183-. 
septic f=a x 7 . Gordan, P. Mth. A. 

31 (1888) 566-. 
septics. BrioscM, F. A. Mt. 26 (1897) 

255-. 
sextic. Maimno, G. [1884-85] Palermo 

Cir. Mt. Bd. 1 (1887) 7-; Mth. A. 30 (1887) 

442-. 

. Gordan, . Erlang. Ps. Md. S. 

Sb. 17 (1885) 40-. 

sextics. Brioschi, F. A. Mt. 1 (1867- 

68) 159. 
Discriminants of binary forms. Bonsdorff, E. 

[E. J.] [1876] Helsingf. Acta 11 (1880) 

191-. 

and resultant of two binary quantics, geo- 
metrical relation. Cayley, A. L. Mth. S. 
P. 5 (1874) 31-. 

resultants of binary forms. Meyer, F. 

Gott. Nr. (1895) 119-, 155- ; Acta Mth. 19 

(1895) 385-. 
Divisors of binary cubics. Pepin, T. C. B. 92 

(1881) 173-. 
Eliminant of two binary quantics. MacMahon, 

(Capt.) P. A. QJ. Mth. 23 (1889) 139-. 
Factions, definition. Cayley, A. B. A. Bp. 

(1875) (Sect.) 10. 
Finite character of number of invariants of 

binary forms. Mertens, F. Crelle J. Mth. 

100 (1887) 223-. 
system of binary forms. Study, 

Erlang. Ps. Md. S. Sb. 
. G 

Md. S. Sb. [19] (1888) 35-. 
invariants of a binary funda- 
mental form. Hilbert, D. Mth. A. 33 (1889) 

223-. 
. Petersen, J. 

Mth. A. 35 (1890) 110-. 
Form system of binary forms. Gordan, P. 

Bpm. Mth. 1 (1877) 12-. 
Generating functions and tables of groundforms 

for binary quantics, calculation. Franklin, F. 

Am. J. Mth. 3 (1880) 128-. 
Geometrical property of invariant II (ah) 2 of a 

binary 2n-ic, etc. Schoute, P. H. Amst. Ak. 
Vs. 7 (1899) 379-; Amst. Ak. P. 1 (1899) 
313-. 

Graphical representation of invariants and co- 
variants, application of new atomic theory. 
Sylvester, J. J. Am. J. Mth. 1 (1878) 

Graphs, Clifford's. Spottiswoode, W. L. Mth. 

S. P. 10 (1878-79) 204-. 
, . Buchheim, A. L. Mth. S. P. 17 (1887) 

, , application to ordinary binary quanti 

Kempe, A. B. [1885] L. Mth. S. P. 17 (18! 

107-, 419. 
, Sylvester-Clifford, application to ordinary 

binary quantics. Kempe, A. B. L. Mth. S. 

P. 24 (1893) 97-. 



Harmonic and equianharmonic polars of binary 
forms. Sclwute, P. H. Amst Ak. Vs. M. 6 
(1889) 277-; As. Fr. C. B. (1889) (Pt. 2) 
100-. 

Hessian of a binary cubic. Fontene, G. N. 
A. Mth. 18 (1899) 459-. 

form, geometrical illustration. 
Schoute, P. H. Amst. Ak. Vs. M. 6 (1889) 
190-. 

, theorem on. Gerbaldi, F. 

Palermo Cir. Mt. Bd. 3 (1889) 22-. 
, . Schoute, P. H. Palermo 

Cir. Mt. Bd. 3 (1889) 160-. 

quantic in terms of the roots. 
McMahon, J. A. Mth. 5 (1889-90) 17-. 

sextic, and discriminant of octavic. 

Maisano, G. Palermo Cir. Mt. Bd. 3 (1889) 
53- ; 4 (1890) 1- ; 5 (1891) 152-. 

covariant of a binary quintic. Lindemann, 
C. L. F. [1882] Mth. A. 21 (1883) 71-. 

covariants of binary biquadratic forms, 
geometric hints for construction. Wedekind, 
L. Erlang. Ps. Md. S. Sb. 7 (1875) 93-. 

, Jacobian, etc., in one dimension geometry. 
Newson, H. B. [1894] Kan. Un. Q. 3 (1895) 
103-. 

of a product of linear functions. Franklin, 
F. J. H. Un. Cir. [9 (1889-90)] 31; A. Mth. 
5 (1889-90) 103-. 

, identical vanishing of. 

Franklin, F. J. H. Un. Cir. [9 (1889-90)] 

77-. 
Higher algebra, theorem in (binary quantics) . 

Russell, E. QJ. Mth. 21 (1886) 373-. 
Identities, linear, between squares of binary 

forms. Meyer, F. W. Mth. A. 21 (1883) 
b. [19] (1888) 31-. 441-. 

Jordan, . Erlang. Ps. Indefinite binary forms with conjugate in- 

determinates. Picard, E. C. B. 97 (1883) 

745-. 
Invariant of binary cubic, expression in terms 

of complete system. Pascal, E. Nap. Bd. 

26 (1887) 245- ; 27 (1888) 67-. 

conditions that two binary quintics may 
have four common roots. Berzolari, L. A. 
Mt. 19 (1891-92) 269-. 

configuration of a binary form. Mertens, F. 
Wien Ak. Sb. 98 (1890) (Ab. 2a) 73.- 

derived forms, mutual actions. Sylvester, 
J. J. Crelle J. Mth. 85 (1878) 89-. 

, direct computation. CJuipman, C. H. [1891] 
J. H. Un. Cir. [11 (1891-92)] 41-. 

forms of a system of binary biquadratics. 
Pascal, E. Nap. Ed. 27 (1888) 402-. 

operations admitting of permutation. Capelli, 
A. Nap. Ac. At. 1 (1888) No. 1, 17 pp. 

processes, on binary fields of higher genus. 
Pick, G. Gott. Nr. (1894) 311-. 

, simultaneous, of a binary quadratic and 

binary biquadratic form. Clebsch, R. F. A. 

[1870] Mth. A. 3 (1871) 262-. 
, quadratic , of two binary forms. Le Paige, 

C. M. M. H. H. Brux. Ac. Bll. 44 (1877 

365-. 

of 10th order of a sextic. Le Paige, 
C. M. M. H. H. Liege S. Sc. Mm. 9 (1882) 
(No. 3) 12 pp. 



cs. 
17 (1887) 



150 



2050 Binary Forms 

Invariant of 12th order of quintic. Fact, de 
Bruno, F. QJ. Mth. 1 (1857) 361-. 

18th order of quintic. Le Paige, 
G. M. M. H. H. C. E. 92 (1881) 241-. 

and solution of quintic equa- 
tion. Hermite, C. Crelle J. 59 (1861) 
304-. 

theory applied to solution of algebraic 
equations. Berger, A. Stockh. Ofv. (1890) 
165- ; Fschr. Mth. (1890) 140. 

of binary forms. Schapira, H. D. Mth. 
Vr. Jbr. 2 (1893) 63-. 

, generating functions. MacMahon, 
(Capt.) P. A. Am. J. Mth. 9 (1887) 189-. 

Invariants of binary biquadratic. Jamet, V. 

N. A. Mth. 19 (1900) 419-. 
forms. Capelli, A. Palermo G. Sc. 

Nt. 15 (1882) 59-. 
. Hilbert, D. Leip. Mth. Ps. B. 

37 (1885) 427-; Mth. A. 28 (1887) 381-. 
. Gordan, . Liouv. J. Mth. 6 

(1900) 141-. 
, etc. (letter to M. Hermite). 

Hilbert, D. Liouv. J. Mth. 4 (1888) 249-. 
for higher transformations. Gordan, 

P. [1868] Crelle J. 71 (1870) 164-. 
, representation. Hilbert, D. Mth. 

A. 30 (1887) 15-. 

in two series of variables, geo- 
metrical interpretation. Kohn, G. D. Nf. 

Vh. (1896) (Th. 2, Hdlfte 1) 5-; D. Mth. Vr. 

Jbr. 5 (1901) (Heft 1) 58-. 
octavic, relation between. Alagna, R. 

Palermo Cir. Mt. Ed. 6 (1892) 77-. 
sextic. Richmond, H. W. QJ. Mth. 

31 (1900) 57-. 
system, relations between. Torelli, G. 

Nap. Ed. 25 (1886) 126-. 
, complete systems, application of symmetric 

functions. Mertens, F. Krk. Ak. (Mt.-Prz.) 

Ez. 2 (1892) 141- ; Fschr. Mth. (1892) 

and covariants of binary forms. Novi, G. 
G. Mt. 2 (1864) 306-, 321-. 

, especially of 3rd and 4th 

degree. Siacci, F. A. Mt. 7 (1865) 73-. 
, law of reciprocity. Sylvester, 

J. J. C. E. 86 (1878) 446-. 
quartic considered as two ternary 

quadrics. Burnside, W. S. [1869] QJ. Mth. 

10 (1870) 211-. 
, fundamental, of binary forms, method 

for obtaining ensemble of. Sylvester, J. J. 

C. E. 84 (1877) 1113-, 1211-. 
, irreducible, of binary forms, higher 

limit to number. Sylvester, J. J. C. E. 86 

(1878) 1437-, 1491-, 1519-. 
, to binary quintic, synoptical table. 

Sylvester, J. J. Am. J. Mth. 1 (1878) 

370-. 
, rule for calculating number. Sylvester, 

J. J. [1878] Mess. Mth. 8 (1879) 1-. 

of equation of nth degree. Studnicka, F. U, 
Casopis 10 (*1881) 208- ; Fschr. Mth. 
(*1881) 130. 

, fundamental, of binary octavic. Sylvester, 
J. J. C. E. 84 (1877) 240-, 532-. 



Binary Forms 2050 

Invariants, fundamental, of binary quantics, 
limits to order and degree. Sylvester, J. J. 
E. S. P. 27 (1878) 11-. 

of given order and degree of binary decimic, 
table of numbers of. Sylvester, J. J. C. E. 
89 (1879) 395-. 

hyperelliptic equations. Brun, F. de. 

Stockh. Ofv. (1897) 173- ; Fschr. Mth. (1897) 

400-. 
integral polynomials, certain. Laisant, 

C. A. Palermo Cir. Mt. Ed. 8 (1894) 249-. 
, irreducible, of the binary quintic and sextic. 

Elliott, E. B. Mess. Mth. 26 (1897) 105-. 
, , degrees 20 and 30 for binary septic. 

Hammond, J. Mth. A. 36 (1890) 255-. 
, method of research for. Elliott, E. B. 

B. A. Ep. (1891) 568. 

of octavic, irreducible relations among. 
Alagna, R. Palermo Cir. Mt. Ed. 10 (1896) 
41-. 

, Prof. Malet's, identification with Sir James 

Cockle's criticoids. Harley, (Rev.) R. E. 

S. P. 38 (1885) 45-. 
, , . Malet, J. C. E. 

S. P. 38 (1885) 211-. 
, rational, of binary form. Alexejeic, W. G. 

Fschr. Mth. (1899) 110-. 
, representation by B functions. Bolza, O, 

Gott. Nr. (1887) 418- ; Mth. A. 30 (1887) 

478-. 

of simplest simultaneous binary forms. 
Bessel, A. [1868] Mth. A. 1 (1869) 173-. 

simultaneous, of binary forms. Gordan, P. 
Mth. A. 5 (1872) 595-. 

, , and resultant of two binary forms of 

orders 6 and 3. Ovidio, E. d'. Tor. Ac. Sc. 

At. 28 (1893) 20-. 
, , of two binary forms of orders 5 and 4, 

and their resultant. Ovidio, E. d'. Em. 

E. Ac. Line. Mm. 4 (1887) 607-. 
, theorem concerning number of. Sylvester, 

J. J. Ph. Mg. 5 (1878) 178-. 

of two binary forms having a common 
factor. Brioschi, F. Erlang. Ps. Md. S. Sb. 
27 (1896) 116-. 

of orders 5 and 2, or 5 and 3. 

Ovidio, E. d\ [1881] Em. S. It. Mm. 4 
(1882) No. 2, 19 pp. 

quartic forms, relations between. 
Ovidio, E. d\ Tor. Ac. Sc. At. 15 (1879) 
471-. 

Involution. Hesse, L. 0. [1863] Crelle J. 

63 (1864) 179-. 
Involutions determined by quartic.corresponding 

points. Walker, J. J. [1870] L. Mth. S. P. 

3 (1869-71) 69-. 

equations, recurring formula in. Weyr, E. 
Casopis 9 (*1880) 279- ; Fschr. Mth. (*1880) 
544-. 

, cubic. Le Paige, C. M. M. H. H. Wien 

Ak. Sb. 81 (1880) (Ab. 2) 845-; 83 (1881) (Ab. 

2) 351-. 
, higher, and invariants of binary forms. 

Le Paige, C. M. M. H. H. Brux. Ac. Bll. 

44 (1877) 231-. 
, , multiple points. Le Paige, C. M. M. H. H. 

Brux. Ac. Bll. 46 (1878) 247-. 



151 



2050 Binary Forms 

Irreducible forms of cubo-biquadratic system, 

true number of. Sylvester, J. J, C. B. 87 

(1878) 445-. 
Isobaric functions , binary and modified . Trudi , 

N. G. Mt. 12 (1874) 110-. 
Jacobian of a biquadratic and a quadratic. 

Giordano, G. G. Mt. 35 (1897) 349-. 
Jerrard's transformation and combinants. 

Igel, B. Wien Ak. D. 53 (1887) (Ab. 2) 155-. 
Linear substitution, formulae for. Elliott, 

E. B. B. A. Kp. (1894) 581. 

transformations, theory of. Boole, G. Camb. 
and Dubl. Mth. J. 6 (1851) 87-. 

Modular transformation of 5th order. Invariant 

theory of its sextic equation. Gordan, P. 

A. Mt. 1 (1867-68) 367-. 
Octahedron, forms connected with. Pittarelli, 

G. Bm. B. Ac. Line. Ed. 4 (1888) (Sem. 1) 

509-. 
Orthogonal concomitants. Vries, J. de. Amst. 

Ak. Vs. 8 (1900) 562- ; Amst. Ak. P. 2 (1900) 

485-. 
Pencils (faisceaux) of binary cubic forms. 

Berzolari, L. Mth. A. 51 (1899) 473-. 

( ) forms with same functional 
determinant. Hilbert, D. Leip. Mth. Ps. B. 
39 (1887) 112-. 

( ) having same Jacobian. 
StepJianos, C. C. B. 93 (1881) 994- ; Par. 
Mm. Sav. Etr. 27 (1883) No. 7, 138 pp. 

Peninvariants of binary forms. Ocagne, M. d'. 

Brux. S. Sc. A. 11 (1887) (Pt. 2) 314- ; C. B. 

104 (1887) 961-. 
. Perrin, R. C. E. 104 (1887) 

1097-, 1258-. 
. Ocagne, M. d'. C. E. 104 (1887) 

1364-. 
. Perrin, E. [1887] Par. S. Mth. 

Bll. 16 (1888) 82-. 
, principal. Ocagne, M. d'. Par. 

S. Mth. Bll. 16 (1888) 183- . 
Perpetuants. MacMahon, P. A. Am. J. Mth. 

7 (1885) 26-, 259-; L. Mth. S. P. 26 (1895) 

Point covariant with five points, construction 

by ruler. Morley, F. Mth. A. 49 (1897) 

596-. 
Polynomials with 2 variables. Collins, E. 

St. Pet. Ac. Sc. Bll. 2 (1837) 321-. 
Projective involutions. Paolis, E. de. Bm. E. 

Ac. Line. Ed. 2 (1886) (Sem. 2) 335-. 
Quadratic and biquadratic forms, system. 

Harbordt, F. Mth. A. 1 (1869) 210-. 
Quadric transformations. Spottiswoode, W. 

L. Mth. S. P. 16 (1884-85) 148-. 
Quartic, aU+&pH=0, solution. Cayley, A. 

[1868] Mth. A. 1 (1869) 54-. 
Quintic, the B. G. F. for the. Hammond, J. 

J. H. Un. Cir. [5] (1885-86) 37. 
Begular graphs, theory. Petersen, J. Acta 

Mth. 15 (1891) 193-. 
Besultant of a binary quadric and n-ic. White, 

H. S. N. Y. Am. Mth. S. Bll. 1 (1895) 

11-. 
two binary biquadratic forms, reduction 

to fundamental invariants. Warren, J. 

[1865] QJ. Mth. 7 (1866) 67-. 



Binary Forms 2050 



Besultant of two binary biquadratic forms, 
reduction to fundamental invariants. Ovidio, 
E. d\ Tor. Ac. Sc. At. 15 (1879) 385-. 

, and relation between their 

simultaneous invariants. Brioschi, F. Tor. 
Ac. Sc. At. 31 (1895) 299- or 441-. 

cubics. Cayley, A. QJ. Mth. 6 

(1864) 380-. 

forms, various representations. 
Schendel, L. Z. Mth. Ps. 33 (1888) 1-, 65-. 

Besultants. Vanetek, M. N. Prag Sb. (1888) 
(Mth.-Nt.) 152-. 

of binary forms, structure. Netto, E. Gott. 
Nr. (1895) 209-. 

Semi-invariant tables. Cayley, A. Am. J. 
Mth. 7 (1885) 59-. 

for the weights 11 and 12, corrected. 
Cayley, A. Am. J. Mth. 14 (1892) 195-. 

Seminvariants. Cayley, A. QJ. Mth. 19 

(1883) 131- ; 20 (1885) 212-. 
. MacMahon, P. A. Am. J. Mth. 8 (1886) 

. Ocagne, M. d\ Brux. S. Sc. A. 10 (1886) 

(Pt. 2) 75-. 
. Deruyts, J. Liege S. Sc. Mm. 15 (1888) 

No. 4, 11 pp., No. 6, 8 pp. ; Brux. Ac. Bll. 19 

(1890) 255-. 
. Roberts, S. [1890] L. Mth. S. P. 21 (1891) 

219-. 
. Cayley, . QJ. Mth. 26 (1893) 66-. 

of a binary quantic, etc. Elliott, E. B. 
Mess. Mth. 23 (1894) 91-. 

, exact differential expressions connected 
with. Elliott, E. B. Mess. Mth. 25 (1896) 
173-. 

of a given type, Cayley 's number of. 
Elliott, E. B. L. Mth. S. P. 23 (1892) 
298-. 

of infinite form, memoir. Cayley, A. Am. 
J. Mth. 7 (1885) 1-. 

, operators in theory. MacMahon, P. A. 

QJ. Mth. 20 (1885) 362-. 
, some properties. Deruyts, J. Brux. Ac. 

Bll. 13 (1887) 226-. 

and symmetric functions. MacMahon, P. A. 
Am. J. Mth. 6 (1884) 131-. 

, theory. Cayley, A. QJ. Mth. 21 (1886) 

92-. 
Semi- (sub) invariants to binary quantics of 

unlimited order. Sylvester, J. J. Am. J. 

Mth. 5 (1882) 79-. 
Sextic perpetuants for any weight w, proof that 

number of=0. Cayley, A. [1883] (xii) J. 

H. Un. Cir. [3] (1884) 13. 
Steiner's covariant of binary sextic. Maisano, 

G. Mth. A. 31 (1888) 493-. 
. Ovidio, E. d'. Tor. Ac. Sc. 

At. 24 (1889) 164-. 
Sylvester's canonical form of binary quantics, 

degree 2n - 1. Booth, W. QJ. Mth. 20 (1885 

270-. 
Symbol of operations in the theory of forms. 

Brioschi, F. Mil. I. Lomb. Ed. 22 (1889) 

117-. 
Symbolic calculus in theory of binary forms. 

Pascal, E. G. Mt. 26 (1888) 33-, 102-. 

notation of Aronhold and Clebsch. Osgood, 
W. E. Am. J. Mth. 14 (1892) 251-. 



152 



2050 Binary Forms 

Symbolic notation of binary forms. Kluyver, 
J. C. N. Arch. Wisk. 20 (1893) 97-. 

representation of syzygants and covariants. 
Stroh, E. Mth. A. 36 (1890) 262-. 

Syzygants of binary sextic forms. Stroh, E. 

Mth. A. 34 (1889) 306-. 
, fundamental, of binary quintic. Stroh, E. 

Mth. A. 34 (1889) 354-. 
, irreducible, of binary sextic. Gall, (Frhr.) 

von. Mth. A. 35 (1890) 63-. 
, , two simultaneous cubic forms. 

Gall, (Frhr.) von. Mth. A. 31 (1888) 

of two simultaneous binary biquadratic 
forms. Gall, (Frhr.) von. Mth. A. 33 

(1889) 197- ; 34 (1889) 332-. 
. Stroh, E. Mth. A. 36 

(1890) 154-. 
. Gall, (Frhr.) von. 

Mth. A. 43 (1893) 550-. 
Syzygies for the binary sextic, new, obtained by 

Aronhold's operation. Ovidio, E. d'. Tor. 

Ac. Sc. At. 28 (1893) 118-. 
, some classes of binary. Ovidio, E. d'. Tor. 

Ac. Sc. At. 28 (1893) 447-. 
Tables of binary cubic forms. Cayley, A. QJ. 

Mth. 11 (1871) 246-. 
generating functions and groundforms of 

binary duodecimic. Sylvester, J. J. Am, J. 

Mth. 4 (1881) 41-. 
for binary quantics of first 



Ternary Forms 2060 

Transformation and reduction of binary forms. 

Silva, D. A. da. Lisb. Mm. 3 (1851) (Sc. 

Ex.) 1-. 
Transvectants from powers of quadratic. 

Berzolari, L. Palermo Cir. Mt. Ed. 12 

(1898) 258-. 
Transvection of binary forms, fundamental 

property. Stroh, E. Mth. A. 33 (1889) 61-. 
and its geometric significance. 

Pittarelli, G. G. Mt. 16 (1878) 225-; 17 

(1879) 160-. 
Twisted cubic curve, representation of binary 

cubic and quartic forms by. Berzolari, L. 

Palermo Cir. Mt. Ed. 5 (1891) 9-, 33-. 
, forms of fifth order on. Waelsch, E. 

Wien Ak. Sb. 100 (1891) (Ab. 2a) 803-. 
Weierstrassian formulae applied to binary 

quartic and ternary cubic. Baker, H. F. 

QJ. Mth. 24 (1890) 1-. 



2060 Ternary forms. 

Aronhold, theorems, generalisation. Gundel- 

finger, S. [1870] Crelle J. 73 (1871) 175-. 
Biternary forms with contragredient variables. 

Clebsch, R. F. A., d- Gordan, P. [1868] 

Mth. A. 1 (1869) 359-. 
Characteristics of conic sections. Study, E. 

Mth. A. 27 (1886) 58-. 



ten orders. Sylvester, J. J. Am. J. Mth. , Cremona's formula for. Study, E. Mth. 



2 (1879) 223-. 
simultaneous binary 

quantics of first four orders, taken two and 

two together. Sylvester, J. J. Am. J. Mth. 

2 (1879) 293-, 324-. 
, reduced and representative for 

certain ternary systems of binary forms. 

Sylvester, J. J. Am. J. Mth. 5 (1882) 241-. 
, syzygy, for binary quantic. Hammond, J. 

Am. J. Mth. 8 (1886) 19-. 
Tamisage, case of failure in Sylvester's theory. 

Hammond, J. [1882] L. Mth. S. P. 14 

(1882-83) 85-. 
, . Cayley, A. L. Mth. S. 

P. 14 (1883) 88- ; (xn) J. H. Un. Cir. [2] 

(1883) 85-. 

Transformation of algebraic equations by co- 
variants. Brioschi, F. Mth. A. 29 (1887) 

327-. 

binary biquadratic form to form con- 
taining only even powers. Hesse, L. O. 

Crelle J. 41 (1851) 243-. 
cubic form into sum of cubes. Hesse, 

L. 0. Crelle J. 38 (1849) 262-. 
form, higher. Cayley, A. Mth. A. 

4 (1871) 359-. 

forms and of the corresponding in- 
tegrals. Brioschi,. Em. E. Ac. Line. Ed. 4 

(1895) (Sem. 1) 363-. 
of order not prime. Meyer, F. W. 

Mth. A. 21 (1883) 528-. 
quantics. Grow, (Miss) B. E. [1900] 

N. Y. Am. Mth. S. Bll. 7 (1901) 3, 12-. 
elliptic integral to Weierstrass's form. 

Pittarelli, G. Em. E. Ac. Line. Ed. 4 (1888) 

(Sem. 1) 703-. 



A. 27 (1886) 102-. 
, revision of Study's theory. Zeuthen, H. G. 

Mth. A. 37 (1890) 461-. 
Combinant N of the ternary cubic. Maisano, G. 

Palermo Cir. Mt. Ed. 4 (1890) 153-. 
Combinants of three ternary quadrics. Gerbaldi, 

F. Tor. Ac. Sc. At. 25 (1890) 390-. 
Common tangents of Hessian and Cayleyan of 

curve. Maisano, G. [1885] Palermo Cir. 

Mt. Ed. 1 (1887) 46-. 
Concomitants of ternary cubic, the 34. Cayley, 

A. Am. J. Mth. 4 (1881) 1-. 
cubics. Dingeldey, F. Mth. A. 31 

(1888) 157-. 
forms, the associated. Brunyate, W. E. 

QJ. Mth. 25 (1891) 155-. 
three ternary quadrics. Baker, H. F. 

Camb. Ph. S. T. 15 (1894) 62-. 
Conditions that a quadric may be one-signed. 

Nanson, E. J. Mess. Mth. 25 (1896) 157- ; 

26 (1897) 57-. 
Covariant conies and cubics of plane cubic. 

White, H. S. N. Y. Am. Mth. S. T. 1 (1900) 

of 9th order of ternary cubic form, geometric 
significance. Gerbaldi, F. Tor. Ac. Sc. At. 
15 (1879) 707-. 

S of plane quartic, theorem on. Giant, E. 
Palermo Cir. Mt. Ed. 14 (1900) 16-. 

Covariants of plane cubic. Gordan, P. N. Y. 

Am. Mth. S. T. 1 (1900) 9-. 
sixth degree of ternary quartic. Maisano, 

G. Palermo Cir. Mt. Ed. 1 (1887) 54-. 
Curves analogous to Hessians, Steinerians, and 

Cayleyans. Maisano, G. Palermo Cir. Mt. 
Ed. 1 (1887) 66-. 



153 



2060 Ternary Forms 

Cyclicants or ternary reciprocants, and allied 
functions. Elliott, E. B. L. Mth. S. P. 19 
(1889) 377-. 

Differential equations of pure ternary re- 
ciprocants. Elliott, E. B. L. Mth. S. P. 
18 (1886-87) 142-. 

operators, certain linear, interchange of 
variables in. Elliott, E. B. [1889] Phil. 
Trans. (A) 181 (1891) 19-. 

Discriminant of ternary cubic forms. Mangeot, 

S. N. A. Mth. 12 (1893) 421-. 
form. Gordan, P. Munch. Ak. Sb. 

17 (1888) 477-. 
, order of. Roberts, S. [1869] L. 

Mth. S. P. 3 (1869-71) 14-. 
Eliminant of set of general ternary quadrics. 

Muir, T. [1899] Edinb. B. S. T. 39 (1900) 

667-; 40 (1905) 23-. 

Generating functions of ternariants, essay to- 
wards the. Forsyth, A. R. L. Mth. S. P. 

29 (1898) 487-. 
Hessian covariant of a ternary form. Wolffing, 

E. Mth. A. 36 (1890) 97-. 

of product of two ternary forms. Gerbaldi, F. 
Palermo Cir. Mt. Ed. 3 (1889) 60-, 280. 

Hessians and Cayleyans of cubic curves. Gor- 
dan, P. N. Y. Am. Mth. S. T. 1 (1900) 402-. 

of ternary quantics, identical vanishing. 
Manning, H. P. J. H. Un. Cir. [9 (1889-90)] 
78. 

Invariant of a quadratic bi-ternary form. 
Cayley, A. Crelle J. 57 (1860) 139-. 

system of a ternary cubic form. Mertens, F. 
Wien. Ak. Sb. 97 (1889) (Ab. 2a) 437-. 

ternary forms. Mertens, F. Wien 

Ak. Sb. 95 (1887) (Ab. 2) 942-. 

of trilinear ternary form. Pasch, M. Mth. 
A. 52 (1899) 127-. 

Invariants and covariants of ternary forms, 

properties. Bernardi, G. [1880] G. Mt. 19 

(1881) 136-, 258-. 
, simultaneous, from which resultant of 

3 ternary quadratic forms is composed. 

Igel, B. Wien Ak. Sb. 77 (1878) (Ab. 2) 

783-. 

of 3 ternary quadratic forms. Mertens, F. 
Wien Ak. Sb. 93 (1886) (Ab. 2) 62-. 

Involution AF+BG + GH=0, where the letters 

denote ternary quadrics. Cayley, A. Mess. 

Mth. 22 (1893) 182-. 
Irrational covariant cubics of plane cubics. 

White, H. S. N. Y. Am. Mth. S. T. 1 

(1900) 170-, 508. 
Jacobian of net of quadrics. Schoute, P. H. 

Kazan S. Ps.-Mth. Bll. 9 (1900) 1-, (Prot.) 

33. 
3 ternary forms. Gerbaldi, F. G. Mt. 

27 (1889) 33-. 
Number of proper ternary n-ics. Cunningham, 

(Lt.-Col.) A. Mess. Mth. 23 (1894) 1-. 
Plane cubic curves. Gerbaldi, F. Palermo 

Cir. Mt. Ed. 7 (1893) 19-. 
Quadratic forms, reduction, with proof of See- 

ber's theorem on reduced ternary forms. 

Lebesgue, V. A. Liouv. J. Mth. 1 (1856) 

Eesultant of three ternary quadratic forms. 
Cayley, A. Crelle J. 57 (1860) 139-. 



Ternary Forms 2060 



Eesultant of three ternary quadratic forms. 

Hermite, C. Crelle J. 57 (1860) 371-. 
. Radan, R. N. A. Mth. 8 

(1869) 358-. 
. Gordan, P. Liouv. J. Mth. 

3 (1897) 195-. 
Eesultants of ternary forms. Gordan, P. 

Mth. A. 50 (1898) 113-. 
Ternariants, algebraically complete systems. 

Forsyth, A. R. Am. J. Mth. 12 (1890) 1-, 

115-. 
Ternary cubic form. Tanner, H. W. L. L. 

Mth. S. P. 27 (1896) 187 -. 

, resolution into factors, conditions. 
Walker, J. J. [1865] QJ. Mth. 7 (1866) 
272-. 

, linear factors. Spottiswoode, 

W. QJ. Mth. 7 (1866) 281-. 
, 3 linear factors, conditions. 

Brioschi, F. A. Mt. 7 (1876) 189-. 

, transformation to canonic form. 
Spottiswoode, W. [1863] Crelle J. 63 (1864) 
244-. 

, . Brioschi, F. C. E. 81 

(1875) 590-. 

forms. Cayley, A. Camb. and Dubl. 
Mth. J. 1 (1846) 97-. 

. Aronhold, S. H. Crelle J. 39 (1850) 

140- ; 55 (1858) 97-. 
. Hermite, C. Liouv. J. Mth. 3 

(1858) 37-. 

. Brioschi, F. C. E. 56 (1863) 304-. 

. Clebsch, R. F. A., <& Gordan, P. 

[1868] Mth. A. 1 (1869) 56-. 
. Gundelfinger, S. Mth. A. 4 (1871) 

144-. 
. Clebsch, R. F. A., & Gordan, P. 

Mth. A. 6 (1873) 436-. 
arising from division of circle. Eisen- 

stein, G. Crelle J. 28 (1844) 289- ; 29 (1845) 

19-. 
, canonic transformation, property of 

parameter. Brioschi, F. L. Mth. S. P. 12 

(1880-81) 58-. 

, relation between 2. Cayley, A. 
Ph. Mg. 20 (1860) 512-. 

, theory. Harnack, A. Mth. A. 9 

(1876) 218-. 

and quartic forms. Hesse, L. 0. Crelle 

J. 41 (1851) 285-. 

definite forms. Hilbert, D. Acta Mth. 17 



form, conditions of decomposition. Hada- 
mard, . Bordeaux S. Sc. PV. (1896-97) 
100-. 

, representation by linear combination of 

2 others. Bertini, E. Mil. I. Lomb. Ed. 
24 (1891) 1095-. 

forms. Eisenstein, G. Liouv. J. Mth. 17 
(1852) 473-. 

. Simerka, W. Wien SB. 38 (1859) 390-. 

. Brioschi, F. A. Mt. 15 (1887-88) 

235-. 
, any degree. Battaglini, G. Nap. At. 

Ac. 4 (1869) (No. 3) 38 pp. 

and Aronhold's invariants. Sylvester, 
J. J. Ph. Mg. 5 (1853) 299-, 367-. 

154 



2060 Ternary Forms 

Ternary forms, conditions for linear factors 
of. Brill, A. [1896-97] D. Mth. Vr. Jbr. 5 
(1901) (Heft 1) 52- ; Mth. A. 50 (1898) 157-. 

of 4th, 5th, 6th, 7th orders, equations 
arising from certain. Brioschi, F. Mil. I. 
Lomb. Ed. 17 (1884) 401-. 

, Hilbert's method of deriving invariants, 
etc. White, H. S. Am. J. Mth. 14 (1892) 
283-. 

, property. Brioschi, F. G. Mt. 1 (1863) 

65-. 
, reduced systems. Bonsdorff, E. Hel- 

singf. Acta 14 (1885) 397-. 
with several series of variables. Capelli, 

A. G. Mt. 18 (1880) 17-. 
, simultaneous, equivalent to given ternary. 

Forsyth, A. E. QJ. Mth. 23 (1889) 102-. 

linear forms. Study, E. Mth. A. 30 (1887) 
120-. 

quadratic forms. Battaglini, G. [1867] 
Nap. At. Ac. Sc. 3 (1866-68) (No. 17 e No. 26) 
26 + 32 pp. 

, automorphic transformation. Her- 

mite, C. Crelle J. Mth. 78 (1874) 325-. 
, complete invariantive system of three. 

Fischer, E., d- Mumelter, K. Mh. Mth. Ps. 

8 (1897) 97-. 
.indefinite. Picard,E. C.E.97(1883) 

845-. 
, linear syzygetic relations between 

coefficients. Genese, E. W. B. A. Ep. (1882) 

452-. 
, positive, reduction. Charve, L. Par. 

c. Norm. A. 9 (1880) (Suppl.) 156 pp. 
, representation by squares. Igel, B. 

[1874] A. Mt. 6 (1875) 141-. 

, simultaneous reduction of 2, to 
canonical form. Vogt, H. N. A. Mth. 15 
(1896) 441-. 

, system of 2. Perrin, E. Par. S. 

Mth. Bll. 18 (1890) 1-. 
, simultaneous. Osgood, W, F. 

Am. J. Mth. 14 (1892) 262-. 
, 3. Ciamberlini, C. G. Mt. 24 

(1886) 141-. 

, simultaneous. Gundel- 
finger, S. [1874] Crelle J. Mth. 80 (1875) 73-. 

, theory. Meyer, A. Crelle J. Mth. 

98 (1885) 177- ; 112 (1893) 87-. 

quartic f=x^x 2 + x./x 3 + x/x 1 , complete 
form system of. Gordan, P. Mth. A. 17 
(1880) 217- ; 20 (1882) 487-. 

f=x l s x 2 + x<?x 3 + x 3 s x 1 , typical repre- 
sentation. Gordan, P. Mth. A. 17 (1880) 
359-. 

quartics. Joubert, P. C. E. 56 (1863) 1045-, 
1088-, 1123-. 

. Scherrer, F. E. A. Mt. 10 (1880-82) 

212-. 
, invariant systems of. Maisano, G. G. 

Mt. 19 (1881) 198-. 

and quaternary cubic forms. Poincare, H. 
Par. EC. Pol. J. 31 ( = Cah. 50) (1881) 199- ; 
Cah; 51 (1882) 45-. 

Vanishing determinants of 3rd degree, in 
ternary linear forms. Pasch, M. Mth. A. 
44 (1894) 89-. 



Algebraic Forms 2070 

Vanishing functional determinants, ternary 

forms with. Pasch, M. Mth. A. 18 (1881) 

93-. 
Weierstrassian formulae applied to binary quartic 

and ternary cubic. Baker, H. F. QJ. Mth. 

24 (1890) 1-. 

2070 Special developments asso- 
ciated with forms in more than 
three variables. 

Algebraic forms, finite invariant system. Hil- 

bert, D. Gott. Nr. (1888) 450- ; (1889) 25-, 

423-; Mth. A. 36 (1890) 473-. 
, . Gordan, P. Gott. Nr. (1899) 

240-. 
Biquadratic (quadri-quadric) forms. Frobenius, 

G. Crelle J. Mth. 106 (1890) 125-. 
Characteristic determinant of any n quantics, 

property. MacMahon, P. A. B. A. Ep. 

(1900) 644. 
Covariants of quadratics. Mertens, F. Krk. 

Ak. (Mt.-Prz.) Pam. 12 (1886) 1-; Fschr. 

Mth. (1886) 103-. 
Equation connected with quadrics. Sauvage, L. 

N. A. Mth. 14 (1895) 369-. 
Hermite's form, transformation. Loewy, A. 

Gott. Nr. (1900) 298-. 
Hessian of composite quaternary cubic form. 

Walker, J. J. [1865] QJ. Mth. 7 (1866) 

347-. 
a quaternary function. Cayley, A. QJ. 

Mth. 12 (1873) 193-. 

manifoldness in space of 4 dimen- 
sions. Ascione, E. G. Mt. 31 (1893) 210-. 

Invariant systems of quaternary forms. Mer- 
tens, F. Wien Ak. Sb. 98 (1890) (Ab. 2a) 
691-. 

theory of n-ary forms. Pascal, E. Em. E. 
Ac. Line. Ed. 4 (1888) (Sem. 1) 119-. 

Invariants, application of a known theorem to. 

Eosanes, J. Mth. A. 23 (1884) 412-. 
, simultaneous, of two quadratic forms. 

Segre, C. Mth. A. 24 (1884) 152-. 

of 3 quaternary quadratic forms. Mertens, 
F. Wien Ak. Sb. 99 (1891) (Ab. 2a) 367-. 

Jacobian of 4 algebraic surfaces, its singulari- 
ties. Gerbaldi, F. Palermo Cir. Mt. Ed. 10 
(1896) 158-. 

Quadratic form in m variables, decomposition 
into sum of m-n squares. Benoit, . N. 
A. Mth. 5 (1886) 30-. 

with non-vanishing determinant, charac- 
teristic of a real. Loewy, A. Mth. A. 52 
(1899) 588-. 

in n variables, conditions for reduction 

of number. Levy, M. C. E. 86 (1878) 
463-. 

, transformation to n squares. 

Studnicka, F. J. Prag Sb. (1888) (Mth.-Nt.) 
256-. 

forms, adjoint. Eados, G. Mth. Termt. 
Ete. 14 (1896) 26-; Mth. Nt. B. Ung. 14 
(1898) 85-. 

, algebraic theory. Kronecker, L. Berl. 
Mb. (1872) 490-. 



155 



2070 Algebraic Forms 

Quadratic forms, algebraic theory. Darboux, G. 

Liouv. J. Mth. 19 (1874) 347-. 
, families, algebraic reduction. Kronecker, 

L. Berl. Ak. Sb. (1890) 1375- ; (1891) 9-, 

33-. 
, Gauss' s method for canonisation. Somov , 

O. I. [1873] St. Pet. Ac. Sc. Mm. (Rs.) 23 

(* 1874) 26-. 
, symmetric. Schapira, H. D. Mth. Vr. 

Jbr. 3 (1894) 99-. 
, systems (priority question). Jordan, C. 

C. E. 78 (1874) 1763-. 
, theory. Morera, G. Mil. I. Lomb. Ed. 

19 (1886) 552-. 
, . Jamet, V. Mars. Fac. Sc. A. 10 

(1900) Fasc. 5, 18 pp. 

with 2 series of variables. Le Paige, 
C. M. M. H. H. C. K. 94 (1882) 424-. 

and Hermite forms, families of real. Loeicy, 
A. Crelle J. Mth. 122 (1900) 53-. 

n-ary forms. Cauchy, A. L. C. K. 44 (1857) 
361-, 416. 

, criteria for reduction to w-ary (m<n). 

Valyi, G. Mth. Termt. fits. 5 (1887) 226- ; 

Mth. Nt. B. Ung. 5 (1886-87) 16-. 
, multiplication. Huricitz, A. Gott. 

Nr. (1898) 309-. 
Quadrilinear form, and surfaces of the 3rd order. 

Le Paige, C. Brux. Ac. Bll. 8 (1884) 555-. 
Quaternariants, algebraically complete system. 

Mair, D. B. [1894] Camb. Ph. S. T. 16 

(1898) 1-. 
, systems. Forsyth, A. R. Camb. Ph. 

S. T. 14 (1889) 409-. 
Quaternary cubic forms. Salmon, G. Phil. 

Trans. (I860) 229-. 
transformation. Clebsch, A. Crelle 

J. 58 (1861) 109-. 

forms with 2 series of variables. Autonne, 
. Brux. Mm. Cour. 4, 59 (1901) (Pt. 2) 
254 pp. 

7i-ics, number of proper. Cunningham, 
(Lt.-Col.) A. Mess. Mth. 23 (1894) 8-. 

quadratic forms, positive. Korkine, A., (& 
Zolotareff, G. Mth. A. 5 (1872) 581-. 

, , reduction. Charve, L. Par. EC. 

Norm. A. 11 (1882) 119-. 

quartic forms, representation as sums of 10 
biquadratics. Reye, T. Crelle J. Mth. 78 
(1874) 123-. 

Reduction of 2w=(M 11 , U K , ...1^x 1 , x 2 , ...) 2 to 
a sum of squares. Hatliaway, A. S. J. H. 
Un. Cir. [3]'(1884) 57-. 

Semi-covariants of -ary forms. Gallucci, G. 
G. Mt. 35 (1897) 206-. 

Sums of 8 squares, products. (Extension of 
theorem of Euler's.) Young, J. R. Ir. Ac. 
P. 4 (1850) 19-. 

Sylvester's canonical form of quaternary cubic. 
Reye, T. Crelle J. Mth. 78 (1874) 114-. 

System (s<f>-\(/) of quadratic forms. Weier- 
strass's theorem on multiple roots of dis- 
criminant. Hovestadt, H. Z. Mth. Ps. 26 
(1881) 392-. 

Ternary and quaternary linear transformations, 
generating systems. White, H. S. Am. J. 
Mth. 14 (1892) 274-. 



Theory of Equations 2400 

Theory of Equations. 
2400 General. 

Addition-substitutions in algebraic equations. 

Bertelsen, B. P. N. Ts. Mth. 9 (B) (1898) 

84-; Fschr. Mth. (1898) 73. 
Algebraic equation, depression of, owing to 

linear relation between roots. Sayre, H. A. 

[1891] A. Mth. 6 (1891-92) 45-. 

and its derivative, relation between roots. 
Berg, F. J. van den. N. Arch. Wisk. 9 (*1882) 
1-, 60; 11 (1884) 153- ; 15 (1888) 100- ; 
Fschr. Mth. (*1882) 51; (1884) 76; (1888) 

equations. Siebel, A. Arch. Mth. Ps. 56 
(1874) 422-; 57 (1875) 73-, 350- ; 58 (1876) 
127- ; 60 (1877) 138- ; 61 (1877) 122- ; 65 
(1880) 394-; 67 (1882) 375-. 

. w es t, E. C. E. 91 (1880) 598-, 664-. 

, application of form theory to. Szabo, 

P. Orv.-Termt. Ets. (Termt. Szak) (1894) 

153-. 
and an arithmetical progression, theorem. 

Volpicelli, P. N. A. Mth. 14 (1855) 120-. 
Cotes's theorem. Beltrami, E. G. 

Mt. 1 (1863) 123- . 

, rationalisation. Forstemann, W. A. 
Crelle J. 14 (1835) 236-. 

, . Cayley, A. Camb. and Dubl. Mth. 

J. 8 (1853) 97-. 
, theorems. Mathieu, E. N. A. Mth. 15 

(1856) 409-. 

, . Lucas, F. C. E. 78 (1874) 431-. 

, , general. Laguerre, E. N. A. Mth. 

19 (1880) 241-. 
, theory. Brassinne, E. Toul. Mm. Ac. 

1 (1863) 23-. 

, . Konig, J. Mth. A. 21 (1883) 424-. 

, , developments. Kronecker, L. Berl. 

Ak. Mb. (1879) 205-. 

, , an extension. Sylvester, J. J. C. E. 

58 (1864) 689-. 

whose highest powers have small coeffi- 
cients. Morton, W. B. QJ. Mth. 31 (1900) 
247-. 

(repeated) transformation, principle of. 
Schapira, H. Heidi. Nt. Md. Vh. 4 (1892) 
25-. 

transformation. Homer, W. G. [1823] 
Mathematician 1 (1845) 108-, 136-, 311- ; 

2 (1847) 32-, 129-. 

Alternate functions and cyclotomy. Cauchy, 

A. L. C. E. 10 (1840) 178-. 
Coefficients in a transformed equation. Lodge, 

A. Mess. Mth. 12 (1883) 178-. 
Complex magnitudes applied to solution of 

equations. Lerch, M. Casopis 20 (1891) 

265-, 302- ; Fschr. Mth. (1891) 83. 
Construction of equations, historico-critical 

notice. Favaro, A. Mod. Ac. Sc. Mm. 18 



(1878) 127- ; 19 (1879) 233-. 
ubic 



Cubic and higher involutions. Fries, J. de. 

Mh. Mth. Ps. 5 (1894) 1-. 
involutions. Fries, J. de. Palermo Cir. 

Mt. Ed. 5 (1891) 289-; Amst. Ak. Vs. 3 

(1895) 64-. 



156 



2400 



Theory of Equations. General 



Differential operators, use in theory of equa- 
tions. Hammond, J. L. Mth. S. P. 14 
(1882-83) 119-. 

Equation whose roots are functions of roots of 

2 equations. Mackenzie, J. L. Edinb. Mth. 
S. P. 5 (1887) 59-. 

2 roots of given equation. 

Amigues, E, N. A. Mth. 11 (1892) 245-. 
Equations. Adder, . Bordeaux Ac. Se. Pbl. 

(1834) 50-. 
, algebraic theory. Pellet, A. E. Par. S. 

Mth. Bll. 15 (1887) 61-. 
, clearing surds from. All-man, W. [1813] 

Phil. Trans. (1814) 23-. 
, congeneric surd. Horner, W. G. Ph. Mg. 

8 (1836) 43-. 
, identities in theory. Brioschi, F. Tortolini 

A. 5 (1854) 301-. 
, impossible. Cockle, Jas. Ph. Mg. 36 (1850) 

281-. 
, . Finlay, R. Manch. Ph. S. Mm. 9 

(1851) 236-. 
, and surd. Harley, R. Manch. Ph. S. 

Mm. 9 (1851) 207-. 

, infinitesimal theory of, and implicit func- 
tions. Pellet, A. Par. S. Mth. Bll. 23 (1895) 

7-. 

with integral coefficients. Kronecker, L. 
Crelle J. 53 (1857) 173-. 

. Runge, C. Gott. Nr. (1899) 

89-. 
, metaphysics of. Cossali, P. Padova N. 

Sag. 1 (1817) 159-. 

with rational coefficients. Dedekind, R. 
D. Mth. Vr. Jbr. 1 (1892) 33-. 

, rationalisation, direct method. Scheffler, H. 
Grunert Arch. 13 (1849) 389-. 

in tenth book of Euclid's elements. Christen- 
sen, S. A. Ts. Mth. 6 (1889) 161- ; Fschr. 
Mth. (1888) 5. 

, theory. Abbati, P. Mod. Mm. S. It. 10 

(1803) 385-. 
, . Cockle, Jas. Ph. Mg. 27 (1845) 

292-. 
_ t _. Catalan, E. C. C. B. 47 (1858) 

797-. 
, . Becker, J. K. Grunert Arch. 34 (1860) 

288-. 
, . Buys-Ballot, C. H. D. Amst. Vs. Ak. 

13 (1862) 430-. 
, . Cockle, (Sir) J. [1863] Manch. Lt. 

Ph. S. P. 3 (1864) 171-. 
, . Brassinne, E. [1864] Toul. Mm. Ac. 

Sc. 3 (1865) 190-. 
, . Petersen, J. P. C. (xn) Ts. Mth. 1 

(1865) 57-; 3 (1867) 46; 5 (1869) 174- ; 

3 (1879) 170- ; 6 (1882) 3-. 

, . Laurent, H. [Herm.] C. R. 62 (1866) 
140-. 

, , algebraic transformation, and quad- 
ruple algebra. Cockle, Jas. Ph. Mg. 3 (1852) 
436-. 

, , analysis. Cockle, Jas., & Davies, . 
Ph. Mg. 32 (1848) 351-. 

_, _, _. Cockle, Jas. Ph. Mg. 37 (1850) 
493-. 

t ; application of rational mechanics to. 
Lucas, F. C. B. 89 (1879) 224-. 



2400 

QJ. 



Equations, theory, formulae. Hudson, C. 

Mth. 18 (1882) 74-. 
, , general, note. Vieille, J. N. A. Mth. 6 

(1847) 174-. 
, , historical note. Bertrand, J. N. A. 

Mth. 14 (1855) 30-. 
, , . Tortolini, B. C. E. 47 (1858) 

598-. 
, , illustration of theorem. Cayley, A- 

Mess. Mth. 11 (1882) 111-. 
, , synopsis. Cayley, A. Mess. Mth. 5 

(1876) 39-. 
whose roots have their real parts negative. 

Hurwitz, A. Mth. A. 46 (1895) 273-. 
Equivalent equations, some. Taylor, C. QJ. 

Mth. 10 (1870) 93-. 
Fourier's "Analysis," error in. Murphy, R. 

Ph. Mg. 11 (1837) 38-. 
Homogeneous functions of 2 polynomials of the 

same degree. Mirman, L. N. A. Mth. 4 

(1885) 173-. 

"Invention nouvelle en Palgebre " (reproduc- 
tion of 16th century work by Albert Girard). 

Bierens de Haan, D. N. Arch. Wisk. 11 

(1884) 83-. 
Irrationality in solution of f(xyz) = 0.j Enriques > 

F. Em. E. Ac. Line. Ed. 4 (1895) (Sem. 2) 
311- ; Mth. A. 49 (1897) 1-. 

Irrationals, algebraic, theory. Capelli, A . Nap. 

Ed. 30 (1891) 61-. 
Isobaric calculus. Cesdro, E. N. A. Mth. 3 

(1884) 561- ; 4 (1885) 59-, 578. 
Logic of characteristics. Cayley, A. QJ. Mth. 

I (1857) 257-. 

Number of variations of a polynomial whose 

coefficients depend on a parameter. Andre", D. 

Par. EC. Norm. A. 2 (1885) 75-. 
Progressions, geometrical, Euler-Pfaff theorem. 

Grunert, J. A. Grunert Arch. 2 (1842) 

220-. 
, , . Luchterhandt, A. R. Grunert 

Arch. 3 (1843) 305-. 
, , . Gopel, A. Grunert Arch. 

3 (1843) 394-. 

Quadri-quadric porism. Mathews, G. B. QJ. 

Mth. 30 (1899) 16-. 
Quintic surds, 2, rationalisation of expression. 

Tortolini, B. (vm) A. Mt. 4 (1861) 

285-. 
Badicals, removal from equations. Mooney, D. 

[1796] Ir. Ac. T. 6 (1797) 221-. 
, . Hultman, F. W. Ts. Mt. Fys. 

4 (1871) 1-. 

Eational functions of n elements, and general 
theory of equations. Konig, J. [1878] Mth. 
A. 14 (1879) 212-. 

Eeviews of books by Fourier and Drobisch. 
Gartz, . Grunert Arch. 1 (1841) 225-. 

Boots of derived equation, property. Legebeke, 

G. J. [1881] N. Arch. Wisk. 8 (*1882) 75-; 
Arch. Neerl. 16 (1881) 273-. 

System of trigonometrical equations, with 
applications to porisms of coaxal conies. 
Wolstenholme, J. QJ. Mth. 10 (1870) 356-; 

II (1871) 66-. 

Systems of equations with peculiarities. Krey,H. 
[1881] Mth. A. 19 (1882) 497-. 



157 



2410 



Algebraic Equations 



2410 Elements of the theory of 
algebraic equations; existence 
of roots, symmetric functions; 
rational fractions; partial frac- 
tions. 

Algebra, fundamental theorem, proof. Mertens, 

F. Wien Ak. Sb. 97 (1889) (Ab. 2 a) 1505-. 
, , and solution of equations by square 

roots. Vahlen, K. T. Acta Mth. 21 (1897) 

287-. 
Algebraic equation, roots of derivative. Berloty, 

. C. E. 99 (1884) 745-, 832. 
, . Cayley,A. C. R. 110 (1890) 

174-, 215-. 

equations, a law of inertia for. Meyer, F. 
Gott. Nr. (1891) 279-. 

Cauchy's theorem. Zbikovskij, A. K. Kazan 

S. Nt. (Ps.-Mth.) P. 6 (1888) 240-. 
Coefficients in expansions invol /ing symmetric 

expressions. Anglin, A. H. Liouv. J. Mth. 

2 (1886) 139-. 
expressed as functions of sums of like powers 

of roots. Janni, V. Nap. Ed. 18 (1879) 

199-. 

and sums of powers of roots, relations 
between. Cauchy, A. L. C. E. 12 (1841) 
698-, 813- . 

Decomposition of certain expressions into 2 
squares. Realis, S. N. A. Mth. 4 (1865) 
451-. 

Development of an algebraic fraction. Mac- 
Mahon, P. A. Am. J. Mth. 6 (1884) 287-. 

Diaphoric functions. Tanner, H. W. L. Mth. 
Gz. 1 (1900) 152- . 

(Tanner). Genese, E. W. Mth. Gz. 1 

(1900) 184. 

Differences of roots, analytic use. Minich, S. E. 
[1875] Em. E. Ac. Line. At. 3 (1876) (Pt. 2) 
303. 

Differential equations in theory of asym- 
metric algebra. Forsyth, A. E. Camb. Ph. 
S. T. 16 (1898) 291-. 

Discriminant of cubic equation and quadratic 
expression Q 2 - 3PP', relation. Young, J. E. 
[1876] Ir. Ac. P. 2 (1875-77) 744-. 

Equation of differences. Cayley, A, Tortolini 
A. 2 (1859) 365-; Phil. Trans. (1860) 93-. 

7ith order, and system of n equations 

satisfied by roots. Antaev, S. N. [1897-1900] 
Eec. Mth. (Moscou) 20 (1899) 33-; 21 (1901) 
1-; Fschr. Mth. (1897) 92; (1900) 94. 

for product of differences of (all but one) 
roots of an equation. Cayley, A. Phil. 
Trans. (1861) 45-. 

of quotients of roots. Terquem, O. N. A. 
Mth. 4 (1845) 516-. 

with roots in arithmetical progression. 
Viaggi, F. G. Mt. 15 (1877) 376-. 

roots of which are diminished by p, re- 
lations between coefficients. Lobatto, E. 
Amst. Vs. Ak. 4 (1856) 208-. 

, similar functions of roots. Kronecker, L. 
Liouv. J. Mth. 19 (1854) 279-. 



2410 



Equation of squares of differences. Desmarcst, 

E. N. A. Mth. 1 (1842) 169-. 
. Tarnier, . N. A. Mth. 3 

(1844) 410-. 
. Pegado, M. Lisb. A. 2 (1858) 

19-. 

, progressive development. 
Minich, S. E. Yen. At. (1858-59) 343-. 

of roots, existence of relation 

among coefficients. Ellis, E. L. (\iAdds.) 
Gamb. Mth. J. 1 (1839) 256-. 

, and geometrical applica- 
tion to tangents to a curve from one point. 
Joachimsthal, F. N. A. Mth. 9 (1850) 
98-. 

sums of roots taken 2 together. Gerono, 

G. C. N. A. Mth. 2 (1843) 128-. 

with 2 roots rationally expressible in terms 
of others (Brioschi). Genocchi, A. N. A. 
Mth. 16 (1857) 95-. 

Equations with equal differences of roots. 

Gatti, S. [1876] G. Mt. 15 (1877) 28-. 
. Viaggi, F. G. Mt. 15 

(1877) 376-. 
, formulae in theory. Sharp, W. J. C. Mess. 

Mth. 9 (1880) 188-. 
, irreducible, relations of roots. Schane- 

mann, T. [1852] Wien D. 5 (1853) 143-. 
, , (Schonemann) . Ettingshausen, 

A. von. Wien SB. 8 (1852) 442-. 
, proof that roots have form p + q>J-I. 

Crelle, A. L. Berl. Ab. (1829) 1-. 
, resolvability into factors of 1st or 2nd 

degree, Laplace's proof, etc. Hube, K. (vi 

Adds.) Krk. Eoczn. Uniwers. 3 (1818) 92-. 

with roots expressible as linear functions of 
one root. Pellet, A. E. Bll. Sc. Mth. As. 
4 (1880) (Pt. 1) 262-. 

in geometrical progression. Terquem, 

O. N. A. Mth. 5 (1846) 210-. 
progression. Guilmin, A. N. A. 

Mth. 8 (1849) 242-. 
; theorem that complex roots occur in pairs, 

Gauss's proof. Combette, E. (xn) Brest S. 

Ac. Bll. 7 (1871) 28 (bis)-. 
, theory. Gauss, C. F. Gott. Ab. 4 (1848- 

50) 3-. 
, , fundamental principle. Du Bourguet, 

. Gergonne A. Mth. 2 (1811-12) 338-. 
, , . Bret, . Gergonne A. Mth. 

3 (1812-13) 31-. 
, , . Du Bourguet, . Gergonne 

A. Mth. 3 (1812-13) 94-. 
, , . Bret, -. Gergonne A. Mth. 

3 (1812-13) 369-. 

, , . Encontre, D. Gergonne A. Mth. 

4 (1813-14) 201-. 

, , . Liouville, J. Liouv. J. Mth. 4 

(1839) 501- ; 5 (1840)31-. 
, , . Woodtouse, L. G. Teix. J. Sc. 

6 (1885) 177-. 
, , theorem. Hocks, H. Z. Mth. Ps. 

28 (1883) 123-. 
, , , Cauchy's. Eudio, F. Ziir. 

Vjschr. 39 (1894) 345-. 
, , , Mourey's proof. Grunert, J. A. 

Grunert Arch. 1 (1841) 81-. 



158 



2410 Existence of Roots 

Equations, theory, fundamental theorem, 
proof. Stern, M. A. Crelle J. 23 (1842) 
370-. 

, , -- , . Wittstein, T. Grunert Arch. 
11 (1848) 218-. 

Every equation in one unknown can be satisfied 
by a complex value of this unknown, geo- 
metric proof. Wittstein, T. Grunert Arch. 
6 (1845) 225-. 

rational integral function vanishes for some 
real or complex value of variable, proof. 
Stieltjes, T. J. (jun.) N. Arch. Wisk. 9 
(*1882) 196-. 

EXISTENCE OF BOOTS. 

Murphy, E. Ph. Mg. 2 (1833) 60-, 220-. 
Henry, J. (vi Adds.) Ph. Mg. 3 (1833) 417. 
(proof.) Clausen, T. As. Nr. 17 (1840) 325-. 
(__.) Deahna, F. Crelle J. 20 (1840) 337-. 
( .) Eisenstein, G. Crelle J. 29 (1845) 96. 
(_.) Staudt, G. K. C. von. Crelle J. 29 

(1845) 97-. 
( .) Goodwin, H. Camb. and Dubl. Mth. J. 

2 (1847) 224-. 

(_.) Airy, (Sir) G. B. [1858] Camb. Ph. S. 
T. 10 (1864) 283-, 327-. 

Cayley, A. Ph. Mg. 18 (1859) 436-. 
Challis, J. Ph. Mg. 19 (I860) 46-. 
Foscolo, G. G. Mt. 2 (1864) 13-. 
Young, G. P. Cn. J. 9 (1864) 26-. 
De Morgan, A. L. Mth. S. P. 1 (1866) 
No. 6, 1 p.; Camb. Ph. S. P. 1 (1866-67), 
24-. 

( .) Laurent, H. Les Mondes 11 (1866) 438-. 
(_.) Walton, W. [1869] QJ. Mth. 11 (1871) 

178-. 
( .) Clifford, W. K. [1870] Camb. Ph. S. P. 

2 (1876) 156-. 
(_.) Gordan, P. Erlang. Ps. Md. S. Sb. 8 



(1876) 138-. 
( .) Macnie, J. 
80-. 



Des Moines Anal. 5 (1878) 



( .) Malet, J. C. [1878] Ir. Ac. T. 26 (1879) 

453-. 
( .) Mansion, P. (xn) Brux. S. Sc. A. 

4 (1880) (Pt. 2) 99-. 

( .) Netto, E. Crelle J. Mth. 88 (1880) 16-. 
( .) Dutordoir, H. [1882] (xn) Brux. S. Sc. 

A. 7 (1883) (Pt. 1) 52-; (Pt. 2) 437-. 
( .) Mansion, P. (xn) Mathesis 3 (1883) 

(Suppl.) 14 (bis)-. 
(.) Maksimovich, V. P. (xn) Kazan S. 

Nt. (Ps.-Mth.) P. 1 (1883) [No. 7] 49-. 
(_.) WalecM, . N. A. Mth. 2 (1883) 241-. 
( .) Hoist, E. Christiania F. (1886) No. 1, 

8 pp. ; Acta Mth. 8 (1886) 155-. 
(_.) juel, C. Ts. Mth. 5 (1887) 161- ; Fschr. 

Mth. (1887) 70. 
( .) Laisant, C. A. Par. S. Mth. Bll. 15 

(1887) 42-. 
( .) Zeuthen, H. G. N. Ts. Mth. 1 (B) (1890) 

65-; Fschr. Mth. (1890) 105-. 
( .) Amigues, E. C. B. 112 (1891) 212-. 
( .) Brunei, . Bordeaux S. Sc. Mm. 2 

(1891) i-. 
(_.) Carvallo, E. N. A. Mth. 10 (1891) 

109-. 



Existence of Roots 2410 

(proof.) Loria, G. Bb. Mth. (1891) 99- ; (1893) 

47-; Bv. Mt. 1 (1891) 185- ; 2 (1892) 37-; 

3 (1893) 105-. 
( .) Meray, C. Bll. Sc. Mth. 15 (1891) 

236-. 
( .) Phragmen, E. Stockh. Ofv. (1891) 

113-. 
(_.) Weierstrass, K. Berl. Ak. Sb. (1891) 

1085-. 
( .) Mertens, F. Mh. Mth. Ps. 3 (1892) 

293-. 
( .) Mansion, P. Brux. S. Sc. A. 17 (1893) 

(Pt. 1) 65-. 
( .) Bocher, M. N. Y. Am. Mth. S. Bll. 1 

(1895) 205-. 
(_.) Carnoy, J. Em. N. Line. At. 53 (1900) 

167-. 
( .) Lamb, H. Manch. Lt. Ph. S. Mm. & 

P. 43 (1900) A T o. 7, 4 pp. 
d'Alembert's theorem. Brisse, C. Par. EC. 

Pol. J. 56 (1886) 163-. 

. Catalan, E. Bv. Sc. 43 (1889) 265-. 

. Durand-Greville, E. Bv. Sc. 43 (1889) 

266-. 

. Vivanti, J. Bv. Sc. 43 (1889) 267. 

. Lougraire, L. de. Bv. Sc. 43 (1889) 

267-. 

. L. Ev. Sc. 43 (1889) 268-. 

. Delbceuf, J. Ev. Sc. 43 (1889) 269-. 

. Jamet, V. Mathesis 14 (1894) 5-; N. 

A. Mth. 14 (1895) 437-. 
Cauchy's proof, simplification. Sussmann, J. 

Crelle J. 44 (1852) 57-. 
(proof) and Cauchy's theorem on imaginary 

roots. De Morgan, A. [1857] Camb. Ph. 

S. T. 10 (1864) 261-. 
Gordan's proof. Dalwigk, F. von. Mth. A. 

34 (1889) 158-. 
of higher equations. Burg, A. Wien Jb. Pol. 

I. 17 (1832) 141- ; 19 (1837) 155-. 
,2 proofs. Ullherr, J. C. Crelle J. 

31 (1846) 231-. 
proof that every equation has root of form 

p + gv /^I. Ullherr, J. C. D. Nf. Vsm. B. 

(1845) 85-. 
of a rational integral equation. Elliott, E. B. 

L. Mth. S. P. 25 (1894) 173-. 
n roots in every equation of nth degree. 

Scheffler, H. Grunert Arch. 15 (1850) 390-. 
. Valeriani, V. G. Mt. 

[13 (1875)] 33-. 
I . Mandl, M. Wien Az. 

24 (1887) 257-. 
.proof. Challis, J. Ph. 

Mg. 17 (1859) 112-. 
I __ _ , (Challis). Airy, 

G. B. Ph. Mg. 17 (1859) 176-. 
(reply to Airy). 

Challis, J. Ph. Mg. 17 (1859) 283-. 
trinomial and quadrinomial equations. Pineto, 

Z. St. Pet. Ac. Sc. Mm. (Rs.) 9 (*1866) 

254-, 306. 



Expression of x n + y n in powers of (x + y) and 
xy. Gruson, J. P. Berl. Ab. (1814-15) 
(Mth.) 30-. 



159 



2410 



Factors, resolution of integral functions into. 
Bretschtieider, C. A, Arch. Mth. Ps. 46 
(1866) 422-. 

, ----- . Mandl, M. D. Nf. Vh. 
(1894) (Th. 2, Hdlfte 1) 7. 

, resolvability into real simple and quadratic. 
Gauss, C. F. Gott. Cm. 3 (1814-15) 107-, 
135-. 

, ------ . Collins, E. St. Pet. Ac. 

Sc. Bll. 2 (1837) 377-; Crelle J. 18 (1838) 
119-. 

, ------ . Perott, J. Crelle J. 

Mth. 99 (1886) 141-. 

Formula 

(x-a)(x-b)f l (x)=-F(x)+f(x) 

IF (a) x - b F(b)x-a\ 
\f(a)a-b + f(b)b-a\- 

Lemonnier, H. Par. S. Phlm. Bll. 2 (1878) 97-. 
Fractions, a theorem on. Catalan, E. Brux. 

Ac. Bll. 19 (1890) 742-. 
Function aleph, its properties. Dickstein, S. 

Krk. Ak. (Mt.-Prz.) Pam. 12 (1886) (35)-; 

Fschr. Mth. (1886) 121. 
-- , some theorems. Dickstein, S. Krk. Ak. 

(Mt.-Prz.) Pam. 16 (1889) 53-. 
Functions of differences, fundamental fact as 

to. Elliott, E. B. Mess. Mth. 29 (1900) 

180-. 

--- of roots of given equation. Selivanov, 

D. T. Eec. Mth. (Moscou) 15 (1891) 581-. 

-- roots, and coefficients, relations. Dickson, 

J. D. H. Edinb. K. S. T. 29 (1880) 535-. 

of an equation, Newton's identities 
concerning. Saalschvtz, . Konigsb. Schr. 
36 (1895) [5]-. 

Generating function, Borchardt's. Faa de 

Bruno, F. [1875] Crelle J. Mth. 81 (1876) 

217-. 
-- , . Kostka, C. [1876] Crelle J. Mth. 

82 (1877) 212-. 
-- , . ReJwfovsky, V. Casopis 11 (* 1882) 

111-; Fschr. Mth. (*1882) 105-. 
-- of symmetric functions. Meier, F. Brux. 

Ac. Bll. 10 (1860) 608-. 

, symmetric relations found by. Bor- 

chardt, C. W. [1855] Crelle J. 53 (1857) 

193-. 
Homogeneous products, sums, and roots of 

equations, theorems. Horner, J. QJ. Mth. 

6 (1864) 360-. 
Infinite partial fractions, reduction of ex- 

ponential fractions to. Cisa de Gresi, . 

Tor. Mm. Ac. 31 (1827) 225-. 
Integral symmetric functions. Mertens, F. 

Krk. Ak. (Mt.-Prz.) Rz. 1 (1891) 333-; 

Fschr. Mth. (1891) 154-. 
Irrational fractions, rationalisation of denomi- 

nator. Sommer, B. Grunert Arch. 18 (1852) 

Isobaric functions, use in recurring series. 

Pietrocola, C. Nap. Ac. At. 9 (1899) No. 8, 

23pp. 
Jacob! , theorem, general analysis of formula 



Algebraic Equations 



2410 



*& Liouville, J. C. R. 13 (1841) 




Logarithmic derived function of an integral 

polynomial. Laisant, C. A. As. Fr. C. R. 

(1894) (Ft. 2) 208-. 
MacMahon's generalisation of the Newton- 

Girard formulae. Gegenbauer, L. [1900] 

Amst. Ak. Vs. 9 (1901) 332-; Amst. Ak. 

P. 3 (1901) 347-. 
Newton, a formula of. Cesdro, E. Mathesis 

6 (1886) 172-. 
Number of roots, theorem of d'Alembert. 

Delbceuf, J. Rv. S. 42 (1888) 823-. 
Numerical equations, theory. Anon, (xi 53) 

N. A. Mth. 17 (1878) 104-. 
Partial fractions. Franchini, P. [1829] Lucca 

At. Ac. 6 (1830) 173-. 

. Eisenstein, G. Crelle J. 32 (1846) 71-. 

. Meyer, U. H. Grunert Arch. 7 (1846) 

316-, 386-. 
, identities concerning. Schmidt, J. JR. 

Amst. Mengelwerk 2 (1816) 153-. 
, reduction to. Serooskerken, R. C. van T. 

Utr. A. Ac. (1817-18) 67 pp. 
, . De Wit, Ae. Utr. A. Ac. (1817- 

18) 54 pp. 
, . Dirksen, E. H. Crelle J. 1 

(1826) 53-. 
, . Crelle, A. L. Berl. Ab. (1831) 

, . Oettinger, L. Crelle J. 32 (1841) 

63-, 148-. 
, . Amstein, H. Laus. S. Vd. B1L 

17 (1881) 145-. 
, . Hoepflingen-Bergendorf, H. von. 

Arch. Mth. Ps. 66 (1881) 314-. 
, . Steplmnos, C. [1883] Bll. Sc. 

Mth. As. 8 (1884) 120-. 
, , with application to trigonometry. 

Saalschiitz, L. Mh. Mth. Ps. 9 (1898) 132-, 

268. 
, , geometrical meaning of. Eeuschle, 

C. Z. Mth. Ps. 41 (1896) 103-. 
, and their integration, theory. Sauvage,. 

L. Mars. Fac. Sc. A. 2 (1892) 3-. 
, theorems. Mainardi, G. Tortolini A. 

1 (1850) 342- ; 2 (1851) 505-. 
Polynomials approximating to fractional func- 
tions. Cebysev, P. [1892] St. Pet. Ac. Sc. 

Mm. (Rs.) 72 (1893) (Suppl.) No. 7, 13 pp. 
, Jacobi's. Stieltjes, . C. R. 100 (1885) 

620-. 
Power of polynomial, formula for. Piarron de 

Mondesir, E. S. As. Fr. C. R. (1877) 154-. 
Powers of roots, Newton's theorems combined 

in one formula. Torriani, J. E. Lisb. Ac. 

Sc. Mm. (Cor.) 3 (pte. 2) (1814) 1-. 

Rational fraction , \f o2in' decomposition. 

Gerono, G. C. N. A. Mth. 18 (1859) 346. 

, formula of Laplace's. 

Y 



467-. 



Jilrgensen, C. Crelle J. 11 (1834) 136-. 



160 



2410 



Algebraic Equations 



2410 



Eational fractions. Stainville, de. Gergonne 

A. Mth. 3 (1812-13) 279-. 
, algebraic integrals in. Bouniakmvsky, N. 

St Pet. Ac. Sc. Mm. 3 (1833) 205-. 

, approximation to functions of one 
variable by. Laguerre, E. Par. S. Mth. 
Bll. 5 (1877) 78-. 

, decomposition. Stainville, de. Par. 

EC. Pol. Cor. 3 (1814-16) 25-. 
, . Crelle, A. L. Crelle J. 9 (1832) 

231- ; 10 (1833) 42-. 
, . Finck, B. N. A. Mth. 4 (1845) 

295-. 

, . Rawson, R. Mathematician 1 

(1845) 265-; 2 (1847) 6-. 

, . Liouville, J. Liouv. J. Mth. 11 

(1846) 462-. 

, . Terquem, 0. N. A. Mth. 6 (1847) 

, . Montojo, S. Cadiz Period. M. Ci. 

1 (1848) 54-. 
, . Brioschi, F. Crelle J. 50 (1855) 

239-, 318-. 

, . Rouche, E. C. E. 46 (1858) 
540-. 

, . Vieille, J. C. K. 49 (1859) 746-. 

, . Horner, J. [1860] QJ. Mth. 5 

(1862) 39-. 
, . Moch, S. N. A. Mth. 1 (1862) 

339-. 
, . Realis, S. N. A. Mth. 3 (1864) 

438-. 
, . Trudi, N. G. Mi. 2 (1864) 225-, 

257-. 

, . St Germain, A. de. N. A. Mth. 8 



, . Hermite, C. (xn) Brux. S. Sc. A. 

2 (1878) (Pt. 2) 157-. 
, . Gomes Teixeira, F. G. Teix. J. 

Sc. 1 (1878) 5-, 17-, 33-, 49-, 97-, 113- ; 2 

(1880) 33-. 
, . Jamet, V. N. A. Mth. 8 (1889) 

228-. 
, , and theory of residues. Rouche, E. 

C. E. 49 (1859) 863-. 

, transformation. Rangoni, L. 
[1834] Mod. Mm. S. It. 21 (1836) 65-. 

, development in partial fractions. Anon. 

(vi_536) Gergonne A. Mth. 10 (1819-20) 

255. 
, expansion. Trudi, N. (xi) Nap. Ac. 

At. 2 (1865) No. 17, 68 pp. ; (vm) Nap. Ed. 

5 (1866) 441-. 
. Factorials, ratios of reciprocal. Cauchy, 

A. L. C. E. 17 (1843) 921-, 1159-. 
. , , and transformation of 

logarithms into definite integrals. Cauchy, 

A. L. C. E. 17 (1843) 779-. 

, geometric properties. Lucas, F. C. E. 
78 (1874) 140-, 180-, 271-. 

, index. Hermite, C. Par. S. Mth. Bll. 

7 (1879) 128- . 
, theorems by Hermite. Laguerre, E. 

Crelle J. Mth. 89 (1880) 339-. 
, theory. Picquet, H. Par. 6c. Pol. J. 

Cah. 53 (1883) 79-. 

functions of the cubic. Sawin, A. A. Mth. 
9 (1894-95) 158-. 

VOL. I. 161 



Eational functions of roots, form. Realis. S. 

G. Mt. 9 (1871) 206-. 
of integral equation. Blutel, . 

Par. S. Mth. Bll. 20 (1892) 92-. 
Eationalisation of algebraic expressions, 

Scheibner, W. Leip. B. 15 (1863) 63-. 
consisting of sums of square roots 

(Fermat's problem). Lehmann, J. W. H 

Grunert Arch. 35 (I860) 207-. 
any binomial denominator. Decher, G. 

Grunert Arch. 20 (1853) 245-. 

fractions. Unferdinger, F. Grunert 
Arch. 33 (1859) 104-. 

a sum of 2 th roots. Rychlicki, S. Arch. 

Mth. Ps. 68 (1882) 180-. 
Eecurring functions of 3rd degree. Gohierre 

de Longcliamps, . As. Fr. C. E. 9 (1880) 

115-. 
Eegular difference terms. Kempe, A. B. L. 

Mth. S. P. 25 (1894) 343-, 396. 
Eoots of equations, dimensions. De Morgan, A . 

QJ. Mth. 1 (1857) 1-, 80, 232-. 
, expression by transcendental functions 

impossible. Wantzel, L. Par. S. Phlm. PV. 

(1845) 114-. 
, form of. Olivier, L. Crelle J. 1 

(1826) 97-. 

, forms of. Casinelli, A. (s. L.) 
Bologna N. Cm. 8 (1846) 317 

, geometrical representation. Goodwin, 

H. [1846] Camb. Ph. S. T. 8 (1849) 342-. 

, properties. Cockle, Jos. QJ. Mth. 5 

(1862) 291-. 

, property. Brioschi, F. N. A. Mth. 

15(1856)366-. 

, , with geometrical applications. 
Laisant, C. A. As. Fr. C. E. (1888) (Pt. 2) 

, square roots of. Terquem, 0. N. A. 

Mth. 6 (1847) 456-. 

, transformation. Gelder, J. de. 
Amst. Mengelwerk 1 (1816) 46-. 

quadratic with complex coefficients. 
Johnson, . N. Y. Mth. S. Bll. 2 (1893) 
171. 

Successive powers of root, Anglin's formula. 

Cayley, A. QJ. Mth. 19 (1883) 223-. 
Sum of like powers of roots. Faure, H. N. 

A. Mth. 14 (1855) 94-. 
, as function of coefficients. 

Pellet, A. E. N. A. Mth. 14 (1875) 259-. 
, and vice-versa. 

Farkas, J. Arch. Mth. Ps. 65 (1880) 433-. 
Sums of like powers of roots of equations, and 

Brioschi's theorem. Genocchi, A. N. A. 

Mth. 12 (1853) 260- ; 14 (1855) 246-. 
powers of roots of general quadratic. 

Kapteyn, W. N. Arch. Wisk. 3 <*1877) 

203-. 
, Newton's formula, generalisation. 

Lachlan, R. Mess. Mth. 13 (1884) 155-. 
, theorem. Collins, E. [1837] 

St Pet. Ac. Sc. Bll. 3 (1838) 52-. 

, , and application to 
infinite products. Stockier, F. de B. G. 
Lisb. Mm. Ac. Sc. 2 (1799) 1-. 

, , proof. Schubert, F. T. 

[1808] St Pet. Ac. Sc. Mm. 2 (1810) 124-. 



2410 Symmetric Functions 

Sums of powers of roots to (2n-l) th power, to 

construct polynomial from. Laguerre, E. 

Par. S. Mth. Bll. 5 (1877) 26-. 
, Waring' s formula. Janni, V. 

Nap. Ed. 17 (1878) 27-. 
, . Cayley,A. Mess. Mth. 

21 (1892) 133-. 
, . Almeida Arez, J. B. d\ 

G. Teix. J. Sc. 14 (1900) 117- ; Fschr. Mth. 

(1900) 162. 
, and Wronski's aleph function, 

Crocchi's proposition. Dickstein, S. Krk. 

Ak. (Mt.-Prz.) Pam. 12 (1886) (41)-; Fschr. 

Mth. (1886) 121. 

SYMMETEIC FUNCTIONS. 

Cauchy, A. L. [1824] Par. Mm. Ac. Sc. 9 

(1830) 104-. 

Conti, C. Padova N. Sag. 3 (1831) 90-. 
Pioch, A. Brux. Ac. Bll. 2 (1835) 252-. 
Transon, (Prof.) A. N. A. Mth. 9 (1850) 75-. 
Dienger, J. Grunert Arch. 16 (1851) 471-. 
Jaufroid, B. N. A. Mth. 12 (1853) 116-. 
Brioschi, F. Tortolini A. 5 (1854) 313-, 422-. 
Borchardt, C. W. N. A. Mth. 14 (1855) 26-. 
Faa de Bruno, F. Tortolini A. 6 (1855) 338-, 

412-, 476-. 

Kronecker, L. Liouv. J. Mth. 1 (1856) 385-. 
Betti, E. Crelle J. 54 (1857) 98-. 
Cayley, A. Phil. Trans. (1857) 489-. 
Roberts, M. Tortolini A. 3 (1860) 172- ; QJ. 

Mth. 4 (1861) 57-; (vm) A. Mt. 4 (1861) 

50-. 

Matthiessen, L. Z. Mth. Ps. 12 (1867) 322-. 
Bonolis, A. G. Mt. 11 (1873) 321-. 
Faa de Bruno, F. C. B. 76 (1873) 163-. 
Isely, J. P. [1874] Neuch. S. Sc. Bll. 10 (1876) 

59-. 

Malet, J. C. [1874] Ir. Ac. T. 25 (1875) 337-. 
Kapteyn, W. N. Arch. Wisk. 2 (* 1876) 73-. 
Boschi, P. Bologna Ac. Sc. Mm. 7 (1876) 

569-. 

Kronecker, L. Berl. Ak. Mb. (1880) 936-. 
Forsyth, A. R. Mess. Mth. 10 (1881) 44-. 
Durfee, W. P. [1882] (xn) J. H. Un. Cir. [2] 

(1883) 23. 

Biehler, C. N. A. Mth. 3 (1884) 218-. 
Ocagne, M. d\ G. Teix. J. Sc. 7 (1886) 133-. 
Allardice, R. E. Edinb. Mth. S. P. 7 (1889) 

Worontzoff, . N. A. Mth. 10 (1891) 325-; 

12 (1893) 116-. 
Kohn, G. Wien Ak. Sb. 102 (1893) (Ab. 2a) 

199-. 
Brunei, . Bordeaux S. Sc. Mm. 4 (1894) 

Junker, F. Mth. A. 45 (1894) 1-. 

Metzler, W. H. L. Mth. S. P. 28 (1897) 

390-. 
Gordan, P. Mth. A. 52 (1899) 501- ; D. Mth. 

Vr. Jbr. 8 (1900) (Heft 1) 178-. 
algebraic theorem. Mertens, F. Wien Ak. Sb. 

106 (1897) (Ab. 2 a) 422-. 
and alternating functions, genesis. Frisiani, P. 

Mil. Effem. As. (1846) 97-. 
application to tetrahedra. Reiss, M. Quetelet 

Cor. Mth. 10 (1838) 229-. 



Symmetric Functions 2410 

associated quantities. Sylvester, J. J. C. E. 

98 (1884) 779-. 
and binomial theorem. Bret, . Gergonne 

A. Mth. 4 (1813-14) 25-. 
Brioschi's theorem. Sylvester, J. J. C. E. 

98 (1884) 858-. 
calculation. Abbati, P. [1804] Mod. Mm. S. 

It. 12 (1805) 8-. 
. Hammond, J. L. Mth. S. P. 13 (1881-82) 

79-. 

. Laurent, H. N. A. Mth. 6 (1887) 416-. 
Cayley 's proof of rule for degree. Sylvester, 

J. J. Ph. Mg. 5 (1853) 199-. 
class. Kapteijn, W. [1881] Arch. Mth. Ps. 67 

(1882) 102-. 

of permanent. Muir, T. Edinb. E. S. P. 
11 (1882) 409-. 

classes. Garbieri, G. [1882] Yen. I. At. 1 

(1883) 33-. 

classification. Mathews, G. B. QJ. Mth. 25 

(1891) 127-. 

complete. Torelli, G, G. Mt. 5 (1867) 110-. 
, and coefficients of an equation, corre- 
spondence between. Crocchi, L. G. Mt. 20 

(1882) 301-. 
"critical" and Spencian. Cockle, Jas. QJ. 

Mth. 4 (1861) 97-. 
and a determinant of common occurrence. 

Trudi, N. Nap. Ed. 3 (1864) 121-. 
determinant occurring in calculation. Gubler, 

E. Ziir. Vjschr. 35 (1890) 79-. 
determination from coefficients. Kostka, C. 

[1875] Crelle J. Mth. 81 (1876) 281-. 
development by sums of like powers. Janni, V. 

G. Mt. 23 (1885) 34-. 
of differences of roots of an equation. Tannery, 

J. C. E. 98 (1884) 1420-. 
elementary, relations between. Junker, F. 

Mth. A. 38 (1891) 91-. 
, and sums of powers. Junker, F. Z. Mth. 

Ps. 41 (1896) 199-. 
form (x, - X^P, #,, x 2 being roots. Roberts, 

M. N. A. Mth. 19 (1860) 23-. 
formula concerning. Pesci, G. Bologna Ed. 

(1886-87) 49-. 
formulae, 2. Petersen, J. P. C. (xn) Ts. Mth. 

6 (1876) 9-. 
fundamental principle. Gergonne, J. D. 

Gergonne A. Mth. 3 (1812-13) 238-. 
. Bret, . Gergonne A. Mth. 4 (1813- 

14) 25-. 

systems for. Vahlen, K. T. Acta Mth. 23 
(1900) 91-. 

geometric representation. Spitzer, S. [1850] 

Haidinger Ab. 4 (1851) (Ab. 3) 1-. 
and inverse operators. MacMahon, P. A. L. 

Mth. S. P. 15 (* 1883-84) 20-. 
maximal and minimal values, proof of 

theorems of Cauchy. Terquem, 0. Liouv. 

J. Mth. 5 (1840) 37. 
multiplication. Babczynski, T. Z. Mth. Ps. 

17 (1872) 147-. 
. MacMahon, P. A. Mess. Mth. 14 (1885) 

164-. 
of n variables, general theorem. Jung, G. C. 

E. 82 (1876) 988-. 
new theorem. MacMahon, P. A. QJ. Mth. 

20 (1885) 365-. 



162 



2410 Symmetric Functions 

new theory. MacMahon, P. A. Am. J. Mth. 
11 (1889) 1- ; 12 (1890) 61- ; 13 (1891) 193- ; 

14 (1892) 15-. 

Newton's propositions, proof. Steen, A. Ts. 
Mth. 3 (1885) 30-; Fschr. Mth. (1885) 111. 

theorem. Tweedie, C. Edinb. Mth. S. P. 
11 (1893) 61. 

operators. Lachlan, B. L. Mth. S. P. 18 

(1886-87) 39- ; 19 (1889) 294-. 
of pairs of variables. Brill, A. Gott. Nr. 

(1893) 757-. 
partition problem. Lemoyne, G. G. Mt. 10 

(1872) 93-. 
problem. Holmboe, B. M. Mg. Ntvd. 2 (1836) 

279-. 
properties of a complete table. MacMahon, 

P. A. Am. J. Mth. 10 (1888) 42-. 
rational, calculation with. Hoppe,R. Schlomilch 

Z. 4 (1859) 353-. 
relation between forms. Kostka, C. [1881] 

Crelle J. Mth. 93 (1882) 89-. 

, and invariants. Gambioli, D. G. Mt. 
29 (1891) 41-. 

representation by sums of powers. Hankel, H. 

[1865] Crelle J. 67 (1867) 90-. 
of roots and combinations of coefficients of 

weight 11 and 12. Rehofovsky, W. [1882] 

Wien Ak. D. 46 (1883) (Ab. 2) 53-. 
common to several equations. Betti, E. 

Tortolini A. 1 (1858) 193-. 
2 equations. Dewulf, . N. A. 

Mth. 19 (I860) 18-. 
2 equations, representation. Hess, E. 

Z. Mth. Ps. 15 (1870) 325-. 
of a pair of cubic equations. Walker, J. J. 

[1865] Mess. Mth. 3 (1866) 107-. 
and resultants of simultaneous equations. 

Escherich, G. von. Wien Ak. D. 36 (1876) 

(Ab. 2) 251-. 
of systems of equations. MacMahon, P. A. 

[1890] Phil. Trans. (A) 181 (1891) 481-. 
2 equations. Cayley, A. Phil. 

Trans. (1857) 717-. 
, tables to the degree 10. Cayley, A. 

Am. J. Mth. 7 (1885) 47-. 
satisfying partial differential equations. Netto, 

E. Z. Mth. Ps. 38 (1893) 357-. 
and seminvariants. Cayley, A. Am. J. Mth. 

15 (1893) 1-. 

of several series of variables. Junker, F. Mth. 

A. 43 (1893) 225-. 
simple and complete, relation. Crocchi, L. 

[1879] G. Mt. 18 (1880) 377-. 

of sines of angles ( a -\ ] . Johnson, W. W. 

Des Moines Anal. 6 (1879) 105-. 

specified number of roots. Murphy, E. (vi 
Adds.) Ph. Mg. 10 (1831) 413-. 

symbolical representation and invariant charac- 
ters. Gambioli, D. G. Mt. 30 (1892) 
192-. 

tabulation. Durfee, W. P. Am. J. Mth. 5 
(1882) 348-. 

in terms of coefficients. Mainardi, G. Em. 
At. N. Line. 20 (1867) 163-. 

theorem. Cockle, Jas. Ph. Mg. 28 (1846) 
132-. 



Symmetric Functions 2420 

theorem of Cauchy. Bertrand, J. C. B. 45 

(1857) 1-. 
theorems. Analin, A. H. H. [1880-83] Ir. 

Ac. P. 3 (1883) 289-; Edinb. K. S. P. 12 

(1884) 236-. 
theory. Schonemann, T. Crelle J. 19 (1839) 

231-, 289-. 
. Cockle, Jas. Mathematician 3 (1850) 

176-, 246-; Suppl. 27-. 
. Borchardt, C. W. Berl. B. (1855) 165-. 
. Mertens, F. Crelle J. 69 (1868) 289-; 

Wien Ak. Sb. 81 (1880) (Ab. 2) 988-. 
. Anglin, A. H. Crelle J. Mth. 98 (1885) 

175-. 
. Konig, G. Mth. Termt. Ets. 8 (1890) 9-; 

Mth. Nt. B. Ung. 8 (1891) 83-. 
. Mertens, F. Wien Ak. Sb. 108 (1899) 

(Ab. 2a) 473-. 
and theory of distributions. MacMahon, P. A. 

L. Mth. S. P. 19 (1889) 220-. 
of 12 ic , tables. Durfee, W. P. Am. J. Mth. 

5 (1882) 45-. 

13 ic . MacMahon, P. A. Am. J. Mth. 6 
(1884) 289-. 

14 ic . Durfee, W. P. Am. J. Mth. 9 (1887) 
278-. 

two ternary forms. Junker, F. Wien Ak. 
D. 64 (1897) 439-. 

Waring's formula. MacMahon, P. A. Mess. 
Mth. 14 (1885) 8-. 

formulae. Terquem, 0. N. A. Mth. 8 (1849) 
76-. 



Vieille, J. C. B. 44 (1857) 1311-. 
,. . . and differentials of sums of kth 



powers of roots. Serret, J. A. C. B. 45 
(1857) 60-. 



Symmetry of a certain algebraic expression, 
proof. Allardice, R. E. Edinb. Mth. S. P. 
4 (1886) 37. 

, law. MacMahon, P. A. QJ. Mth. 22 (1887) 

Teleological method. Dickstein, S. Prace 

Mt.-Fiz. 3 (1892) 126- ; Fschr. Mth. (1892) 

97-. 
', Wronski's. Krauze, W. Prace Mt.-Fiz. 

3 (1892) 110- ; Fschr. Mth. (1892) 97. 
Wronski's formulae, proof of two. Dickstein, S. 

Krk. Ak. (Mt.-Prz.) Pam. 12 (1886) (87)-; 

Fschr. Mth. (1886) 121. 

2420 Reality, multiplicity, 
separation, of roots. 

Algebra, fundamental theorem and Newton's 

approximation method. Mertens, F. Wien 

Ak. Sb. 101 (1892) (Ab. 2a) 415-. 
Algebraic equations and Campbell's quadratic 

functions. Poulain, A. C. B. 106 (1888) 

470-, 562, 1479. 
, general theorems. Poulain, A. N. A. 

Mth. 6 (1867) 21-. 



163 



L2 



2420 



Reality, multiplicity, separation, of roots 



2420 



Algebraic equations, theorems, 2. Myasoyedov, 

A. N. [1883] (xn) Bee. Mth. (Moscou) 11 

(1883-84) 616-. 
Budan and Fourier's theorem. Fouret, G. N. 

A. Mth. 11 (1892) 82-, 352. 
Sudan's method of extracting roots. Nicholson, 

P. Tilloch Ph. Mg. 60 (1822) 173-. 

theorem concerning roots of an algebraic 
equation. Genocchi, A. Tortolini A. 7 (1856) 
462-. 

Complex roots. Canterzani, S. Verona Mm. 
S. It. 2 (1784) 720-. 

of equations, existence, Hermite's 
proposition, generalisation. Studnicka, F. J. 
Casopis 26 (1897) 95- ; Fschr. Mth. (1897) 95. 

, , proof. Kinkelin, H. Mth. 

A. 1 (1869) 502-. 
, , theorem. Kolbe, J. Wien Sb. 

67 (1873) (Ab. 2) 188-. 
, and factors of polynomials. Wantzel, 

L. N. A. Mth. 3 (1844) 325-. 

numerical equations. Deladereere, 
A., <& Finck, . N. A. Mth. 3 (1844) 41-. 

Conditions that an equation of degree n may 
have only p distinct roots. Antomari, X. 
N. A. Mth. 16 (1897) 63-. 

Continuity of roots. Rouquet, V. N. A. Mth. 
15 (1876) 154-. 

, proof. Bonnet, 0. Bll. Sc. Mth. As. 

2 (1871) 215-. 

Derived equations. Merlieux, E. N. A. Mth. 

3 (1844) 178-. 

polynomials, property. Young, J. R. Ph. 
Mg. 31 (1866) 369-. 

Descartes, Eolle, Fourier, Sturm, and Cauchy, 

theorems of, deduced from one principle. 

Terquem, 0. N. A. Mth. 3 (1844) 188-, 209-, 

555-, 577-. 
Descartes's rule, proof. Tebay, S. (vi Adds.) 

Ph. Mg. 24 (1844) 24-. 
of signs. Terquem, 0. N. A. Mth. 2 

(1843) 248-. 
. Finck, B. N. A. Mth. 3 (1844) 

316-. 
. . Guilmin, A. N. A. Mth. 5 (1846) 

239-, 334-. 



Descartes's rule of signs, generalisation. Gegen- 
bauer, L. Wien Ak. Sb. 83 (1881) (Ab. 2) 321-. 

, lowering limits furnished by. 
Andre, D. C. E. 98 (1884) 212-. 

, theorem in complete algebraic 

polynomials applied to. Jonquieres, E. de. 
C. E. 99 (1884) 1143- . 

theorem, extension. Lucas, E. Par. S. 
Mth. Bll. 8 (1880) 187-. 

Distribution of roots, theorems of Laguerre and 

Myasoyedov. Klark, N. I. (xn) Kazan S. 

Nt. (Ps.-Mth.) P. 1 (1883) \_(No. 8)] 11-. 
Double roots. Guldberg, A. S. Ts. Mth. 4 

(1886) 97-; Fschr. Mth. (1887) 86. 
Electrical determination of roots. Lucas, F. 

C. E. 106 (1888) 195-, 268-, 645-, 1072- ; 

111 (1890) 965-. 
Equal roots. Vachette, A. N. A. Mth. 6 (1847) 

213-. 
. Ostrogradsky, M. A. [1849 j St Pet. 

Ac. Sc. Bll. 8 (1850) 193-. 
. Hudson, G. QJ. Mth. 18 (1882) 215-, 

327-. 
, condition for. Salmon, G, Camb. and 

Dubl. Mth. J. 5 (1850) 159-. 
, theory. Rouche, E. N. A. Mth. 16 

(1857) 66-. 
, . Mansion, . Brux. S. Sc. A. 16 

1892 (Ft. 1) 54-. 
, , and application to tangents to curves. 

Roger, E. N. A. Mth. 3 (1844) 51-. 
Equalities among roots, conditions for existence 

of. Cayley, A. Phil. Trans. (1857) 727-. 
Equality of a given number of roots. Gerono, G. 

C. N. A. Mth. 1 (1842) 90- ; 6 (1847) 75-, 

2 roots, condition. Joachimsthal, F. 
Crelle J. 33 (1846) 371-. 

Equation / 2 (z) + F/ 2 (z) = has all roots imagi- 
nary. Cesdro, E. N. A. Mth. 4 (1885) 
321-. 

Equations with all roots imaginary. Catalan, 
E. C. Liege S. Sc. Mm. 15 (1888) No. 1, 



224-. 

real. Gegenbauer, L. [1881] Wien 

Ak. Sb. 84 (1882) (Ab. 2) 1102-. 

. Zehfuss, G. Grunert Arch. 34 _. Kraus, L. Casopis 15 (1886) 

(1860) 400-. 63 ; Fschr. Mth (1886) 70 

-. Walton, W. QJ. Mth. 5 (1862) J* _L __' _ fcagne M. d\ C. E. 106 
153 -- (1888) 731-. 
Parpaite,-. N. A. Mth. 8 (1869) _ V ! . Selivanov, D. Th. Kazan S. 



. Laguerre, E. N. A. Mth. 18 

(1879) 5-. 
. Poincare, H. C. E. 97 (1883) 

1418-. 
. Jonquieres, E. de. Em. N. Line. 

At. 38 (1885) 55-. 
. Borel,E. Bll. Sc. Mth. 20 (1896) 

327-. 

(Harriot's) rule of signs, demonstration. 
Grunert, J. A. Crelle J. 2 (1827) 335-. 

rule of signs, demonstration (Gauss). 



Ps. -Mth. Bll. 9 (1900) 51-; Fschr. Mth. 

(1900) 94-. 
, class. Clebsch, A. [1861] 

Crelle J. 62 (1863) 232-. 
, . Biehler, C. N. A. Mth. 

19 (1880) 149- ; 6 (1887) 9-. 

, properties. Laguerre, E. 
N. A. Mth. 19 (1880) 224-. 

, of coefficients. Florow, 
P. S. Fschr. Mth. (1898) 70. 

, property. Sylvester, J. J. 
Crelle J. Mth. 87 (1879) 217-. 



signs, demonstration (Gauss). Ger- 

gonne, J. D. Gergonne A. Mth. 18 (1827-28) , source. Fouret, G. C. E. 106 

352-. (1888) 1135-. 

" , extension. Laguerre, E. C. E. , types. Fouret, G. C. E. 106 

92(1881)230-. (1888)1220-. 

164 



2420 



Reality, multiplicity, separation, of roots 



Equations, difference product in case of equal 
roots. Franke, E. [1876] Crelle J. Mth. 83 
(1877) 65-. 

with a given number of complex roots. 
Gegenbauer, L. [1882] Wien Ak. Sb. 87 
(1883) (Ab. 2) 264-. 

no positive root, conditions. Andre, D. 

C. E. 98 (1884) 561-. 
, 3rd & 4th orders, nature of roots, criteria. 

Gaines, R. E. A. Mth. 1 (1900) 111-. 
Fourier and Sturm, theorems. Crelle, A. L. 

Crelle J. 13 (1835) 119-. 

, , graphic representation. Tanner, 

.H.W.L. Mess. Mth. 18 (1889) 95-. 
, theorem on roots of equations and re- 
curring series. Stern, M. A. Crelle J. 9 

(1832) 305-. 
Fourier's rule, proof. Young, J. R. Ph. Mg. 

23 (1843) 6-. 
for real roots. Hill, C. J. D. Lund 

Acta Un. 8 (1871) (Mth.) No. 2, 8 pp. 

theorem on equations. O'Kinealy, J. Ph. 
Mg. 48 (1874) 95-. 

. Sharp, W. J. C. QJ. Mth. 17 

(1881) 132-. 
Functions whose roots separate each other. 

Markow, W. A. Fschr. Mth. (1899) 100. 

. Iwanow, J. J. Fschr. 
Mth. (1899) 100. 

. Markow, W. A. Fschr. 

Mth. (1899) 100- . 
Imaginary and equal roots, criteria. Homer, J. 

[1867] QJ. Mth. 9 (1868) 57-. 

roots. Cauchy, A. L. , Par. S. Phlm. Bll. 



2420 



Imaginary roots, Newton's rule. Sylvester, 
J. J. [1865] L. Mth. S. P. 1 (1866) No. 2, 
16 pp. ; Ir. Ac. T. 24 (1871) 247-. 

, , invariantive criteria for quintic. 

Sylvester, J. J. Phil. Trans. 154 (1864) 
579-. 

, for number. Lobatto, B. Amst. 

Vs. Ak. 9 (1859) 92-. 

, . Minich, S. R. Yen. At. 

11 (1865-66) 127-. 

, , proof. Young, J. R. Ph. 

Mg. 30 (1865) 113-, 289-, 363-; 31 (1866) 
369-; 32 (1866) 121- ; Ir. Ac. P. 10 (1870) 
343-. 

, , Sylvester's theorem. 
Poulain, A. Les Mondes 11 (1866) 16-. 

, , . Genocchi, A. N. 

A. Mth. 6 (1867) 5-. 

, and Sylvester's theorem. Jon- 
quieres, E. de. C. B. 99 (1884) 62-, 111-, 
165-, 269-. 

, , theorem connected with. Syl- 
vester, J. J. [1879] Mess. Mth. 9 (1880) 

, number. Berard, . Gergonne A. 
Mth. 9 (1818-19) 345-. 

, between limits. Dienger, J. Grunert 

Arch. 21 (1853) 361-. 
, , test for. Lobatto, R. Liouv. J. 

Mth. 9 (1844) 295-. 
of numerical equations, number. Anon. 

(vi 529) Gergonne A. Mth. 9 (1818-19) 60-. 
, test for. Lavernede, T. Gard. 

Not. Tr. Ac. (1809) 195-. 



(1817) 5-, 161- ; Par. EC. Pol. J. 11(1820) , . Faade Bruno, F. Liouv. 

(18e cah.) 411-. J. Mth. 15 (1850) 363-. 

, Eolle's theorem extended to. Liou- 
ville, J. Liouv. J. Mth. 9 (1864) 84-. 

Brux. S. 



. Bonnet, O. N. A. Mth. 4 (1845) 236-. 

. Terquem, 0. N. A. Mth. 5 (1846) 141-. 

. Prouhet, E. N. A. Mth. 14 (1855) 199-. 

. Buys-Ballot, C. H. D. Amst. Vs. Ak. 

7 (1858) 316-. 

. Heaivood,P.J. Mth. Gz. No. 4 (1895) 31-. 

. Vaes, F. J. N. Arch. Wisk. 3 (1898) 117-. 

, Budan's criterion. Christie, J. R. Ph. 

Mg. 21 (1842) 96-. 

, Cauchy's theorem, extension. De Mor- 
gan, A. [1857] (DC) Camb. Ph. S. P. 1 
(1866) 194. 

, , proof. Liouville, J., & Sturm, C. 

Liouv. J. Mth. 1 (1836) 278-. 

, , proofs. Stiirm, J. C. F. Liouv. 

J. Mth. 1 (1836) 290-. 

, criteria. Young, J. R. Ph. Mg. 22 
(1843) 186-, 252-; 23 (1843) 450- ; 29 (1846) 
32-. 

, . Colombier, P. A. G. N. A. Mth. 

7 (1868) 308-, 501-. 
of equations of order higher than 4th. 

Carandino, G. G. Arcad. 32 (1826) 90-. 

, existence. Dupre, A. Gergonne A. 
Mth. 18 (1827-28) 68-. 

, . Gergonne, J. D. Gergonne A. Mth. 

19 (1828-29) 124-. 
, _, test. Serret, P. N. A. Mth. 6 

(1847) 200-. 
, limiting values of coefficients for given 

number. Schramm, H. 

(1866) 325-. 



, . Mansion, . 
Sc. A. 13 (1889) (Pt. 1) 42-. 

, rules analogous to Newton's. Minich, 

S. R. Ven. At. 11 (1865-66) 211-. 
, for inferior limit to number. Minich, 

S. R. Ven. At. 11 (1865-66) 309-. 
, theorem. Sturm, J. C. F. N. A. Mth. 

5 (1846) 115-. 
Infinite roots of equations. Gerono, G. C. 

N. A. Mth. 3 (1844) 32-, 85-. 
, and asymptotes. Gerono, G. C. 

N. A. Mth. 4 (1845) 33-. 

Integral functions Y n = II ( y - 2 cos -r |i and 
= 1\ n + l/ 

Sturm's functions. Vries, J. de. Amst. 

Ak. Vs. 4 (1896) 133-. 
Interlacing of functions. Sylvester, J. J. 

Crelle J. Mth. 88 (1880) 1-. 
Laguerre's polynomials, property. Laurent, H. 

N. A. Mth. 19 (1880) 380-. 
Least root, general expression for. Konig, J. 

Mth. A. 9 (1876) 530-. 

roots. Dickson, J. D. H. [1877] Edinb. 
E. S. T. 28 (1879) 119-. 

Limit, inferior, of roots of an algebraic equation. 
Mlasojedov, A. N. Eec. Mth. (Moscou) 12 
(1885) 22-. 

Arch. Mth. Ps. 45 , , . Fouret, . Par. 

S. Mth. Bll. 20 (1892) 4-. 

165 



2420 



Reality, multiplicity, separation, of roots 



commensurable roots. 
N. A. Mth. 18 (1859) 



Limit, superior, of 

Montebello, G. de. 

356-. 
, , negative roots deduced from Newton's 

formula. Vitasse, . N. A. Mth. 18 (1859) 

213-. 
, , positive roots. Mourgues, . N. A. 

Mth. 9 (1850) 108-. 
, , . Gisclard, L. N. A. Mth. 11 

(1852) 107-. 
, , . Gohierre de Longchamps, . 

N. A. Mth. 19 (1880) 71-. 
, , in numerical equations. Len- 

theric, . Gergonne A. Mth. 20 (1829-30) 

297-. 
, , roots, determination. Candeze, G. 

N. A. Mth. 20 (1881) 49-. 
, , , Laguerre's rule. Candeze, G. 

N. A. Mth. 19 (1880) 307-. 
, , of numerical equations, Petersen's 

criterion proved erroneous. Giudice, . 

Palermo Cir. Mt. Bd. 6 (1892) 157-. 
Limits of equations. Piani, D. Bologna N. 

Cm. 3 (1839) 237-. 

to moduli of roots. Dim, U. A. Mt. 1 

(1898) 77-. 

. Petrovitch, M. C. B. 129 

(1899) 583-, 873-. 

of roots. Vene, A. A. Bouen Tr . Ac. (1821) 
97-; Ferussac Bll. Sc. Mth. 4 (1825) 206-. 

. Tillot, J. N. A. Mth. 4 (1845) 

224-. 
. Toussaint, . N. A. Mth. 18 (1859) 

310-. 
. Realis, S. N. A. Mth. 3 (1864) 

477-. 
. Gyory, S. (xn) Mag. Tud. Ak. 

Ets. 1 (No. 6) (1867) 125-. 
. Tranton,A. N. A. Mth. 11 (1872) 

254-. 
. Fouret, . Par. S. Mth. Bll. 20 

(1892) 35-. 
, Descartes' s theorem applied. Fourier, 

J. B. J. Par. S. Phlm. Bll. (1820) 156-, 181-. 

, and determination of commen- 
surable roots. Thibault, . N. A. Mth. 
2 (1843) 517-. 

of equation with only real roots. 

Pleskot, A. Prag Sb. (1897) (Mth.-Nt.) 

No. 37, 9 pp. ; N. A. Mth. 18 (1899) 301- ; 

19 (1900) 144. 
literal equations. Bouvier, L. C. 

Gergonne A. Mth. 16 (1825-26) 54-. 

numerical equations. Bret, . 

Gergonne A. Mth. 6 (1815-16) 112-. 
, approximate. Maiziere, 

de. Gergonne A. Mth. 3 (1812-13) 41-. 

of higher order. Row- 
botham, J. Tilloch Ph. Mg. 63 (1824) 369-. 

, superior, of roots. Rachmanov, P. N. 

Kharkov Mth. S. Com. 4 (1895) 141- ; Fschr. 

Mth. (1893-94) 140. 
, variation, in algebraic equations. Chevil- 

lard, A. J. N. A. Mth. 2 (1843) 343-. 
Multiple roots of algebraic equations. Brioschi, 

. C. B. 121 (1895) 582-. 
, theorem. Sondat, P. N. A. 

Mth. 19 (1900) 25-. 



2420 

Ph. 

N. A. 



Multiple roots, theory. Sylvester, J. J. 

Mg. 18 (1841) 249-. 
Multiplicity of roots. Beynac, F. A. 

Mth. 9 (1850) 317-. 
, amount and distribution. Sylvester, 

J. J. Ph. Mg. 18 (1841) 136-. 

in the octavic equation. Alagna, R. 
Palermo Cir. Mt. Bd. 4 (1890) 287-. 

Nature of roots, Borchardt's proposition. 
Studnicka, F. J. Casopis 27 (1898) 237-; 
Fschr. Mth. (1898) 73. 

Newton and Descartes, rule of signs. Orzabal, 
A. Arg. S. Ci. A. 22 (1886) 39-, 97-. 

Newton-Fourier imaginary problem. Cay ley, 
A. [1879] Camb. Ph. S. P. 3 (1880) 231-. 

method applied to imaginary roots. Cay- 
ley, A. QJ. Mth. 16 (1879) 179-. 

Newton's and Laguerre's criteria for positive 
roots. Venard, C. N. A. Mth. 19 (1880) 

Number of different roots of an algebraic equa- 
tion. Baur,L. Mth. A. 50 (1898) 241- ; 52 

(1899) 113-. 
positive and negative roots. Gauss, C. F. 

Crelle J. 3 (1828) 1-. 
roots between limits. Moigno, F. Liouv. 

J. Mth. 5 (1840) 75-. 
. Grunert, J. A. Grunert Arch. 

1 (1841) 19-, 126-. 
. Hermite, C. Crelle J. 52 

(1856) 39-. 
, logarithmic criteria. Laguerre, 

E. C. B. 93 (1881) 1061-. 
, theorem. Myasoyedov, A. N. [1882] 

(xn) Bee. Mth. (Moscou) 10 (1882-83) (Pt. 1) 

56. 
Beal and imaginary roots of equations of 5th 

order, theory. Sylvester, J. J. C. B. 59 

(1864) 749-, 944-; 60 (1865) 759-. 

roots. Bolzano, B. Prag Ab. 5 (1818) 
60 pp. 

. Terquem, 0. N. A. Mth. 10 (1851) 

180-. 

, absence of. Bellavitis, G. Crelle J. 
50 (1855) 263-. 

, geometrical investigation of number. 
Pincherle, S. Bv. Mt. 3 (1893) 54-. 

between given limits. Realis, S. G. Mt. 

9 (1871) 355-. 

, limit. Gohierre de LongcJiamps, . 
N. A. Mth 18 (1879) 49-. 

, , superior. Paque, A. Liege Mm. S. 

Sc. 10 (1855) 199-. 
, of number. Olivier, L. Crelle J. 

1 (1826) 223-. 
, . Sylvester, J. J. C. B. 60 

(1865) 1261-. 

, in a class of equations. Syl- 
vester, J. J. C. B. 58 (1864) 494-. 

, limits, method of finding. Sylvester, 

J. J. N. A. Mth. 12 (1853) 329-. 

, , theorem. Sylvester, J. J. N. A. 

Mth. 12 (1853) 286-. 

, number. Cauchy, A. L. [1813] Par. 

S. Phlm. Bll. (1814) 95- ; Par. EC. Pol. J. 10 
(1815) (17 e cah.) 457-. 

, between limits. Bonnet, 0. N. A. 

Mth. 6 (1847) 464-. 



166 



2420 



Reality, multiplicity, separation, of roots 



2420 



Eeal roots, number between limits. Petr, K. 

Prag Ceske Ak. Fr. Jos. Kz. (Tfida 2) 6 

(1897) Art. 8, 11 pp. ; Prag Fr. Jos. Ac. Sc. 

Bll. (Mth.-Nt.) 4 (1897) (Pt. 2) 61-. 
-- , --- , Sturm's theorem. Joachims- 

thai, F. Crelle J. 48 (1854) 386-. 
-- , for equation x m -px+q = Q. Regis, 

D. G. Mt. 8 (1870) 226-. 

, series for number. Brioschi, F. N. 
A. Mth. 15 (1856) 264-. 

-- , their upper and lower limits and sepa- 

ration. Steklov, V. A. Kharkov Mth. S. 

Com. 3 (1893) 103- ; Fschr. Mth. (1891) 

94-. 
Eeality of roots. Bjorling, C. F. E. [1868] 

Stockh. Ofv. 25 (1868-69) 241- ; Arch. Mth. 

Ps. 48 (1868) 363-. 
--- . Favero, G. B. G. Mt. 13 (1875) 

249-. 

, conditions. Griveau, A. Les 
Mondes 17 (1868) 214-. 

--- of discriminating cubic. Gerono, G. C. 

N. A. Mth. 11 (1872) 305-. 
---- equation of 3rd order. Grunert, 

J. A. Grunert Arch. 29 (1857) 442-. 

in transformation theory. 
Saalschiltz, . Konigsb. Schr. 38 (1897) 
[17}-. 

----- ( l -^\ 
\l-ixj 

C. A. As. Fr. C. E. (1882) 102-. 

-- important equation, new proof. 
Gravelaar, N. L. W. A. [1875] Arch. 
Mth. Ps. 58 (1876) 301-. 

---- quintic, invariant criteria. Harris, 

E. A. A. Mth. 5 (1889-90) 217-. 
----- , -- . Petr, K. Prag Ceske 

Ak. Fr. Jos. Ez. (Tfida 2) 8 (1899) Art. 23, 
12 pp. ; Fschr. Mth. (1899) 103. 
---- secular equation, proof by Fourier's 
method. Sylvester, J. J. Crelle J. Mth. 88 
(1880) 4-. 



Laisant, 



Eoots of cubic, criteria. Vyvyan, T. G. Mth. 
Gz. 1 (1900) 39. 

, equal numerically, of opposite sign, cri- 
teria. Mtiller, F. Arch. Mth. Ps. 46 (1866) 
32-. 

of an equation, limits to. Gob, A. Mathesis 

9 (1889) 269-. 

, multiplicitity of, and a limit to. 
Demoulin, A. Mathesis 9 (1889) 268-. 

equations. Spitzer, S. Grunert Arch. 

25 (1855) 137-. 

, analysis. Murphy, E. Phil. Trans. 

(1837) 161-. 

with complex coefficients. Hermite, 

C. Crelle J. 53 (1857) 182-. 

, elementary representation and inspec- 
tion. Bjnrling, C. F. E. Ts. Mt. Fys. 1 
(1868) 119-. 

with integral coefficients. Cauchy, 

A.L. C. E. 24 (1847) 407-. 

, nth degree, with application to bi- 
quadratic. Mossbrugger, L. Grunert Arch. 
28 (1857) 205-. 

, surd. Moon, E. Camb. Mth. J. 3 

(1843) 20-. 

, theorems. Fleury, L. L. Cherb. 

Mm. S. Sc. 8 (1861) 373-. 

, new formulae relative to. Silva, J. A. M. 
da. [1882] G. Teix. J. Sc. 4 (1883) 3-. 

, number satisfying a given condition. 
Cauchy, A. L. G. E. 40 (1855) 1329-. 

, theory. Bourget, J. N. A. Mth. 9 (1870) 
505-. 

_, _. Bjorling, C. F. E. Stockh. Ak. Hndl. 

10 (1871) (No. 3) 53 pp. 

Eule of signs, new theory. Meech, L. W. 

Des Moines Anal. 2 (1875) 81-, 97-. 
Eules of signs, combinations of four. Sylvester, 

J. J. C. E. 61 (1865) 282-. 
Separation of nearly equal roots. Christie, J. E. 

Ph. Mg. 21 (1842) 96-. 
real roots of equation. Schramm, Ht 

Grunert Arch. 36 (1861) 420-. 



, theorem. Korteweg, D. J. N. Arch. equations. Ovejero, J. Arg. S 



Wisk. 4 (1899) 46-. 

and signs of roots. Du Bourguet, . Par. 
S. Phlm. Bll. (1815) 14-. 

Eolle's theorem. Collin, J. N. A. Mth. 20 

(1881) 132-. 
, and an application. Biehler, C. N. A. 

Mth. 6 (1887) 75-, 190-. 

, extension. Boer, F. de. Amst. Ak. 
Vs. M. 19 (1884) 384-; Arch. Neerl. 19 
(1884) 207-. 

, . McCulloch, J. F. A. Mth. 4 
(1888) 5-. 

, generalisation. Lucas, F. C. E. 106 

(1888) 121-. 

, Lagrange's, and Cauchy's, geometri- 
cally equivalent. Mansion, P. [1875] Mess. 
Mth. 5 (1876) 34-. 

Boot-limitation, Cauchy's theorems, geometri- 
cal representation. Cayley, A. [1874] 
Camb. Ph. S. T. 12 (1879) 395-. 

Eoots, commensurable, criteria. Mathieu, E. 
N. A. Mth. 16 (1857) 145-. 

, fractional, criteria. Terquem, 0. N. A. 
Mth. 4 (1845) 397-. 



Ci. A. 27 (1889) 169-. 
roots. Dirksen, E. H. Berl. Ab. (1835) 

337-. 
. Umpfenbach, Dr. Crelle J. 20 

(1840) 60-. 
. Transon, A. N. A. Mth. 7 (1868) 25-, 

57-. 
. Bjorling, C. F. E. Ups. N. Acta S. 

Sc. 7 (1870) (No. 7) 35 pp. 
. Maleyx, L. N. A. Mth. 11 (1872) 

404- ; 13 (1874) 385-. 

. Laurent, H. N. A. Mth. 14 (1875) 37-. 

. Mlasojedov, A. N. [1884] Eec. 

Mth. (Moscou) 12 (1885) 433- ; Fschr. Mth. 

(1885) 63. 
of certain equations. Laguerre, E. 

G. E. 92 (1881) 178-. 
, improved statement of rule, and new 

theorem. Sylvester, J. J. Ph. Mg. 31 (1866) 

214-. 
, Laguerre 's theorem. Lucas, E. N. 

A. Mth. 19 (1880) 145-. 
, . Levy, L. N. A. Mth. 19 

(1880) 148. 



167 



2420 



Reality, multiplicity, separation, of roots 



Separation of roots by method of differences. 

Desboves, A. H. N. A. Mth. 13 (1854) 

60-. 
. Capelli, A. Nap. Ed. 

33 (1894) 191-, 214-. 

, method, and Lagrange's formula. 
Pellet, A. E. Bll. Sc. Mth. As. 5 (1881) 
(Pt. 1) 393-. 

of numerical equations. Zinna, A. 

G. Mt. 6 (1868) 344-. 
. Laguerre, E. C. E. 89 

(1879) 635- ; 92 (1881) 1146-. 
some equations. Markov, A. A. 

Kharkov Mth. S. Com. (1885) 89- ; Fschr. 

Mth. (1886) 161. 
, and superior limit. Laguerre, E. 

N. A. Mth. 19 (1880) 49-, 97-. 
Signs and nature of roots. Anon, (vi 537) 

Gergonne A. Mth. 10 (1819-20) 341-. 
Sturmians, class of. Chrystal, G. [1881] 

Edinb. E. S. T. 30 (1883) 161-. 
Sturm's functions. Cayley, A. Liouv. J. 

Mth. 11 (1846) 297- ; 13 (1848) 269-. 

. Brioschi, F. N. A. Mth, 13 (1854) 71-. 

. Gilbert, P. Liouv. J. Mth. 12 (1867) 

-87-. 

. Brioschi, F. C. E. 68 (1869) 1318-. 

-T- . Kronecker, L. Berl. Ak. Mb. (1878) 

95-. 
, auxiliary, relation to roots of an equation. 

Sylvester, J.J. B. A. Ep. (1841) (pt. 2) 23-. 

, calculation by determinants. Lemonnier, 
H. C. E. 80 (1875) 252-. 

, coefficients expressed as determinants. 

Heal, W. E. A. Mth. 2 (1885-86) 85-. 
, determination of a series from a single 

determinant. Vleck, E. B. van. [1899] 

A. Mth. 1 (1900) 1-. 

, formulae for equations of 2nd, 3rd, 
and 4th orders. Koralek, P. N. A. Mth. 
11 (1852) 333-. 

, functions analagous to. Lemonnier, H. 

Par. S. Mth. Bll. 6 (1878) 149-. 
, . Miasojedov, A. N. 

Eec. Mth. (Moscou) 12 (1885) 461- ; 

Mth. (1885) 63-. 
and their reciprocal relations. Kronecker, 

L. Berl. Mb. (1873) 117-. 
of 2nd species. Wendlandt, H. Arch. 

Mth. Ps. 62 (1878) 1-. 
, series of. Gegenbauer, L. Amst. Ak. 

Vs. 5 (1897) 185-. 
, . Vries, J. de. N. Arch. Wisk. 

3 (1898) 40-. ' 
, substitutes for. Mollanie, V. Nap. Ed. 

22 (1883) 256-. 
, Sylvester's theorem on. Sturm, J. C. F. 

Liouv. J. Mth. 7 (1842) 356-. 
, . Turazza, D. Yen. At. 11 

(1865-66) 419-. 
and syzygies between rational integral 

functions. Sylvester, J. J. Phil. Trans. 

(1853) 407-. 
, tables for equations of 2nd, 3rd, 4th, and 

5th orders. Cayley, A. Phil. Trans. (1857) 

733-. 
, theorem of Cayley's, proof. Zeipel, E. 

V. von. QJ. Mth. 3 (1860) 108-. 



2420 

N. 



Sturm's method, application. Biehler, C. 
A. Mth. 19 (1880) 76- ; 6 (1887) 421-. 

of finding real roots, expressions for 

?uotients in. Sylvester, J. J. B. A. Ep. 
L853) (pt. 2) 1-. 

separation of roots, modification. 
Nazimov, P. [1885] Eec. Mth. (Moscou) 
13 (1886) 119- ; Fschr. Mth. (1886) 71-. 

quotients, explicit values. Sylvester, J. J. 
Ph. Mg. 6 (1853) 293-. 

remainders. Heilermann, . Crelle J. 43 
(1852) 43- ; 48 (1854) 190-. 

. Faa de Bruno, F. Tortolini A. 7 

(1856) 313-. 

series. Gegenbauer, L. Wien Ak. Sb. 81 

(1880) (Ab. 2) 576-. 

theorem. Terquem, 0. N. A. Mth. 2 
(1843) 97-. 

. Badon-Ghijben, J. (vn) Amst. N. 
Ws. Ntk. Vh. 1 (1844) 89-. 

. Mourgues, . N. A. Mth. 9 (1850) 

278-. 
. Borchardt, C. W. N. A. Mth. 11 

(1852) 403-. 

. Hermite, C. C. E. 36 (1853) 294-. 

. Bertrand, J. C. E. 43 (1856) 1108-. 

. Kronecker, L. C. E. 68 (1869) 1078-. 

. Hattendorff, K. Gott. Nr. (1873) 779-. 

. Darboux, G. Bll. Sc. Mth. As. 8 

(1875) 56-, 92-. 
. Janni, V. G. Mt. 20 (1882) 166-. 

. Nieivenglowski, B. N. A. Mth. 9 

(1890) 181-. 

. Willotte, H. Toul. Ac. Sc. Mm. 3 

(1891) 44-. 

, application. Spiller, . Mth. Misc. 2 

(1839) 133-. 
, . Candioti, M. R. Arg. S. Ci. A. 27 

(1889) 201- . 

, to transformations of binomial 
equations. Sturm, J. C. F. Liouv. J. Mth. 
7 (1842) 132-. 

, determination of X n . Young, J. R. Ph. 

Mg. 7 (1835) 454-. 
, extension. Phragmgn, E. C. E. 114 

(1892) 205-, 440. 

, to system of equations. Bendixson, I. 

[1892] Stockh. Ak. Hndl. Bh. 18 (Afd. 1) 

(1893) No. 2, 18 pp. 

and limits of roots of equation. Sylvester, 

J. J. Ph. Mg. 5 (1853) 446- ; 6 (1853) 14-, 

138-, 210-. 
, Ostrogradski's. Desboves, A. H. N. 

A. Mth. 6 (1867) 348-. 
, proof. Ettingshausen, A. von. Baum- 

gartner Z. 7 (1830) 444-. 

, . Trudi , N. G. Mt. 1 (1863) 59-. 

, remarks. Candeze, G. N. A. Mth. 20 

(1881) 193-. 

, simplification of calculations. Housel, 

. N. A. Mth. 6 (1867) 351-. 

theorems of comparison. BocJier, M. N. 
Y. Am. Mth. S. T. 1 (1900) 414-. 

Variations, number gained or lost in multiplica- 
tion of f(x) by x n a. Andre, D. C. E. 99 
(1884) 182-. 

, in multiplication by x - a. Andrt, D. 

C. B. 98 (1884) 292-. 



168 



2430 



Equations of the lower orders, etc. 



2430 Equations of the second, 
third and fourth orders : other 
particular equations. 

Abelian cubics and symmetrical equations. 

Cockle, Jas. QJ. Mth. 5 (1862) 237-. 
Algebraic equations. Jonquieres, E. de. C.E. 

99 (1884) 345-, 450, 469-, 483-, 546. 
. Lalanne, L. C. E. 99 (1884) 463-. 

, especially irreducible case of Cardan's 
formula. Gegenbauer, L. Liege S. Sc. Mm. 
2 (1900) A r o. 10, 6 pp. 

, pair. Mansion, P. Mess. Mth. 7 (1878) 57-. 

, solution by radicals and by series. Favero, 

G. B. Em. E. Ac. Line. Mm. 6 (1889) 415-. 

whose first member satisfies a linear 
differential equation of the 2nd order. 
Laguerre, E. C. E. 90 (1880) 809- ; 94 (1882) 
412-, 508- . 

resolution of equations, theory. Giudice, F. 
Ev. Mt. 2 (1892) 193-. 

Anharmonic-ratio sextic. Cayley, A. QJ. 

Mth. 10 (1870) 56-. 
Binary equations of 4th or 5th order, conditions 

for 3 equal roots, etc. Cayley, A. Phil. 

Trans. 158 (1868) 577-. 
Continued roots. Dixon, T. S. E. Des Moines 

Anal. 5 (1878) 20-. 
De Moivre, class of equations solved by, and 

their derivatives. Realis, S. N. A. Mth. 4 

(1865) 209-, 289-. 
De Moivre' s formula. Barsotti, G. Lucca At. 

Ac. 17 (1860) 149-. 
theorem and Cardan's formula applied to 

equations. Barsotti, G. Pisa A. Un. Tosc. 

Sc. Cosm. 5 (1858-61) 99-. 
Equation, roots of which are products in pairs 

of roots of another equation. Malet, J. C. 

QJ. Mth. 13 (1875) 30-. 
, 2 given equations. 

Malet, J. C. [1878] A. Mt. (1878-79) 306-. 

, (-); r=0, 1, 2...n. Siacci, 

F. G. Arcad. 18 (1860) 166-. 

for secular inequalities of planetary motion, 
Cauchy's theorem that roots are essentially 
real. Hermite, C. C. E. 41 (1855) 181-. 

with variable parameter, roots. Cauchy, 
A. L. C. E. 12 (1841) 1133-. 

Equations, certain reducible types. Spitzer, S. 
Wien SB. 8 (1852) 422- ; Grunert Arch. 22 
(1854) 1-. 

depending on numerical functions. [Bou- 
gaieff, N. F.] Bugaev, N. V. [1874] (xn) 
Eec. Mth. (Moscou) 7 (1874-75) (Pt. 1) 424-; 
(rx) Bll. Sc. Mth. As. 10 (1876) 102-. 

determining functions of double argument. 
Hill, C. J. D. Crelle J. 11 (1834) 241-. 

, first 4 orders, solution. Eisenstein, G. 
Crelle J. 27 (1844) 81-. 

of form x 3 -bx = l. Lockhart, J. Mathe- 
matician 2 (1847) 253-, 319-. 

x* + ax 2 + bx + c = 0, solution. Leire, 
P. (xn) Ts. Mth. 1 (1877) 117-. 

+ &c. = 0. Laguerre, E. 



C. E. 93 (1881) 890-. 



2430 



Equations of form (xP - a") \f/(x) = Q. Berloty 

. N. A. Mth. 1 (1882) 173-. 
(a, b, c, d) = (a 2 , b 2 , c 2 , d*), solution. 

Cayley, A. Mess. Mth. 15 (1886) 59-. 
(a, b, c - ) = (aP, IP, c" - ), solution. 

Vivanti, G. G. Mt. 27 (1889) 229-. 
() = (), . Tanner, H. W. L. 

Mess. Mth. 19 (1890) 118-. 

_ <J(x-a)(x-b) + J(x-c)(x-d) = e, 

solution. Dickson, J. D. H. Edinb. Mth. 

S. P. 9 (1891) 13-. 
, general theory and application to curves. 

Sdderblom, A. Ups. Arsk. (1879) 64 pp. 

OL.. 

, roots of which are of form cos or 

n 

O7._ 

sin . Johnson, W. W. Des Moines Anal. 

6 (1879) 17-. 

soluble by Cardan's method. Guldberg, 
A. S. Ts. Mth. 3 (1885) 39-; Fschr. Mth. 
(1885) 74. 

, solution of certain. Allardice,B.E. Edinb. 
E. S. P. 17 (1891) 139-. 

Equations, 2nd order. 

Matthewson, R. E. Camb. (M.) Mth. M. 2 

(1860) 232-. 
Marrecas Ferreira, L. F. G. Teix. J. Sc. 2 

(1880) 77-. 
adfected, solution. - Seers, J. Ph. Mg. 4 (1828) 

125-. 
, by goniometry. Mollweide, C. Zach 

M. Cor. 22 (1810) 43-. 
depression. Noel, J. N. Liege Mm. S. Sc. 8 

(1853) 94-. 

general. De Morgan, A. Mathematician 3 

(1850) 154- ; Suppl. 4-. 
, reduction. S., W. J. Camb. and Dubl. 

Mth. J. 5 (1850) 286-. 
with imaginary coefficients, solution. Grunert, 

J. A. Grunert Arch. 8 (1846) 65-. 
invariants. Routh, E. J. QJ. Mth. (v) 6 

(1864) 270-, (vra) 308-. 
maxima and minima, process for determining. 

Shreve, S.H.V. Nost. Eng. Mg. 15 (1876) 530-. 
numerical. Bugaev, N. V. (xn) Eec. Mth. 

(Moscou) 8 (1876) (Pt. 1) 239-. 
paradox. Anon, (vi 556) Gergonne A. Mth. 

15 (1824-25) 118-. 
rational solutions, expression. Tist, . Les 

Mondes 23 (1870) 770-. 
reality of roots. Cayley, A. [1862] Crelle J. 

61 (1863) 367-. 
relation between roots and coefficients. Baehr, 

G. F. W. [1869] Amst. Vs. Ak. 4 (1870) 

(Ntk.) 197-. 
solution. Mathews,G.B. Nt. 57 (1897-98) 463-. 

by trigonometry. Grunert, J. A. Grunert 
Arch. 1 (*1841) 12-. 

(Grunert). Mensing, . Grunert 
Arch. 1 (1841) 189-. 

theorem. Lebesgue, V. A. N. A. Mth. 13 

(1854) 412-. 

theory. Gay, J. Laus. Bll. S. Vd. 1 (1842- 

45) 388-. 
. Macfarlane, A. Am. As. P. (1897) 54. 



169 



2430 Equations, 3rd order 

Equations, 2nd, 3rd and 4tth orders. 

applications of theory of forms. Tortolini, B. 

Tortolini A. 6 (1855) 433-. 
with complex coefficients. Denzler, W. Ziir. 

Vjschr. 4 (1859) 37-. 

rational roots. Sinram, T. Arch. Mth. Ps. 
66 (1881) 94-. 

root-forms, general. Matthiessen, H. F. L. 

Z. Mth. Ps. 24 (1879) 32-. 
solution. Machmcetz, J. Bohm. Gs. Ab. 12 

(1863) 325-. 
. Matthiessen, L. Schlomilch Z. 8 (1863) 

133-. 
. Sinram, T. Arch. Mth. Ps. 64 (1879) 

296-. 
. Ravut, . As. Fr. C. E. (1894) (Pt. 2) 

285-. 

by function r(x). Guldberg, A. S. Chris- 
tiania F. 14 (1872) 144-. 

symmetric solutions. Levanen, S, Helsingf. 

Acta 19 (1893) No. 9, 14 pp. 
trigonometric solution. Cagnoli, . N. A. 

Mth. 9 (1850) 374-. 

Equations, 3rd order. 

Homer, W. G. Thomson A. Ph. 9 (1817) 378-. 
Grunert, J. A. Grunert Arch. 5 (1844) 417- ; 

6 (1845) 1-, 428-. 

Lebesgue, V. A. N. A. Mth. 8 (1849) 219-. 
Grunert, J. A. Grunert Arch. 22 (1854) 347- ; 

30 (1858) 231-. 

Catalan, E. C. C. B. 54 (1862) 659-. 
Eisenlohr, F. C. K. 55 (1862) 64-. 
Fame, H. N. A. Mth. 3 (1864) 116-. 
Sivering, J. N. A. Mth. 5 (1866) 356-. 
D g. Ts. Mt. Fys. 2 (1869) 19-. 
Laguerre, . N. A. Mth. 9 (1870) 343-. 
Le Besgue, V. A. N. A. Mth. 9 (1870) 529-. 
Andre, D. N. A. Mth. 14 (1875) 556-. 
Liebrecht, E. Arch. Mth. Ps. 59 (1876) 217. 
Barbour, L. G. Des Moines Anal. 5 (1878) 73-. 
Eealis, S. N. A. Mth. 17 (1878) 178-. 
Sinram, T. Arch. Mth. Ps. 68 (1882) 106-. 
Barbour, L. G. Des Moines Anal. 10 (1883) 

115-. 

Sawin, A. M. Science 2 (*1883) 44. 
Cayley, A. Mess. Mth. 15 (1886) 62-. 
Giudice, F. Bv. Mt. 3 (1893) 146-. 
Sidler, G. Bern Mt. (1898) 57-. 
Sochocki, J. Wiad. Mt. 3 (1899) 119- ; Fschr. 

Mth. (1899) 102-. 
automorphic transformation. Aubry, A. N. 

A. Mth. 6 (1887) 175-. 
Cardan's formula. Grunert, J. A. Grunert 

Arch. 40 (1863) 246-. 
. Bouniakowsky, V. Crelle J. 3 (1828) 

347-. 
, expansion in series for irreducible case. 

VoU, W. Oken Isis (1826) 678-. 
generalised. Miiller, J. H. T. Grunert 

Arch. 22 (1854) 16-. 
(Halcken). Grunert, J. A. Grunert 

Arch. 14 (1850) 132-. 
, historic note. Forestier, C. Toul. Ac. 

Sc. Mm. 6 (1874) 254-. 



Equations, 3rd order 2430 

Cardan's formula, imaginaries in. Bernardi, 

G. Padova N. Sag. 3 (1831) 184-. 
, transformations. Berndtson, B. Stockh. 

Ac. Hndl. 36 (1815) 183-. 
rule, and general solution of equations. 

Gyory,S. (xn) Mag. Ak. Ets. (Mth. Term.) 

2 (1861-62) 81-. 
, new deduction. Szokol, P. (xn) Orv. 

Term. fits. 8 (1883) (Term. Szak) 273-. 
Chasles's homography, problem. Hesse, L. 0. 

[1862] Crelle J. 62 (1863) 188-. 
and Delian problem ; trisection of an angle. 

Nissen, H. N. Ts. Mth. 1 (A) (1890) 2-, 40 ; 

Fschr. Mth. (1890) 111-. 
equation for squared differences of roots. 

Cayley, A. QJ. Mth. 3 (1860) 307-. 
expression for remaining roots. Young, J. R. 

Ph. Mg. 34 (1849) 193-. 
extension of theorem of Grunert's. Toeplitz, J. 

Grunert Arch. 31 (1858) 222-. 
general. Stainville, de. Gergonne A. Mth. 

9 (1818-19) 197-. 
. Borden, J. Des Moines Anal. 5 (1878) 

110-. 
geometric representation. Thiele, T. N. Ts. 

Mth. 2 (1884) 11- ; Fschr. Mth. (1884) 86. 
giving principal planes of conicoids, etc. Hum- 
bert, E. As. Fr. C. B. (1888) (Pt. 2) 145-. 
and higher, solution. Kulik, J. N. Bohm. 

Gs. Ab. 11 (1861) 21-. 
integral roots. Eealis, S. N. A. Mth. 14 

(1875) 289-, 424-. 
Kramp's treatment. Miiller, J. H. T. Grunert 

Arch. 8 (1846) 107-. 
literal, limits of roots. Rees, R. van. Quetelet 

Cor. Mth. 5 (1829) 30-. 
for principal axes of quadric surface. Kummer, 

E. E. G. Arcad. 98 (1844) 71-. 
, condition for 2 equal roots. 

Jacobi, C. G. J. G. Arcad. 99 (1844) 3-. 
problem of Tortolini. Matthiessen, L. Arch. 

Mth. Ps. 47 (1867) 460-. 
with rational coefficients. Kronecker, L. Crelle 

J. 56 (1859) 188-. 
rational roots. Liebrecht, E. Arch. Mth. Ps. 

60 (1877) 216-. 
real roots. Sawin, A. M. Science 2 (*1883) 

158-. 
reality of roots. Roche, E. N. A. Mth. 1 

(1842) 511-. 

. Tarnier,. N. A. Mth. 3 (1844) 161-. 

relations between roots of certain. Berger, A. 

Ups. S. Sc. N. Acta 18 (1900) No. 3, 14 pp. 
residual. Bouniakmvsky, V. St Pet. Ac. Sc. 

Mm. 2 (1833) 373-; 3 (1838) 13-. 
roots. Barbarin, . As. Fr. C. B. (1887) 

(Pt. 2) 126-. 
, criteria. Kerz, F. Arch. Mth. Ps. 41 

(1864) 68-; 42 (1864) 121- ; 44 (1865) 1-, 

129-, 379-; 45 (1866) 14-; 47 (1867) 363-. 
of which are the sides of a triangle. Zbi- 

kovskij, A. K. Kazan S. Nt. (Ps.-Mth.) P. 5 

(1887) 182- ; Fschr. Mth. (1887) 78. 
solution. Meredith, T. [1791] Ir. Ac. T. 7 

(1800) 69-. 
. Ivory, J. [1799] Edinb. B. S. T. 5 (1805) 

99-. 



170 



2430 Equations, 3rd order 

solution. Berndtson,B. Stockh. Ac. Hndl. 27 

(1806)269-; 28(1807) 72-. 
. Cockle, Jas. Camb. Mth. J. 2 (1841) 248-; 

3 (1843) 28-. 
. Bretschneider, C. A. Grunert Arch. 4 

(1844) 410-. 
. Dippe, M. C. Grunert Arch. 7 (1846) 

149-. 
. Schlesicke, W. Grunert Arch. 11 (1848) 

345-. 
. Rutherford, W. Mathematician 3 (1850) 

257-. 
. Campbell, T. J. Ir. Ac. P. 6 (1853-54) 

352-. 
. Azzarelli, M. Tortolini A. 6 (1855) 

467-. 

. Spitz, C. Grunert Arch. 32 (1859) 435-. 
. Veriot, E. C. B. 60 (1865) 556-. 
. Talbot, W, H. F. Edinb. E. S. T. 24 

(1867) 573-. 
. Thiele, T. N. (xn) Ts. Mth. 4 (1868) 

65-. 

. Alexandre, R. N. A. Mth. 9 (1870) 293-. 
. Gundelfinger, S. [1870] Mth. A. 3 (1871) 

272-. 

. Dahl, C. (xn) Ts. Mth. 4 (1874) 135-. 
. Azzarelli, M. Em. N. Line. At. 31 (1878) 

355-. 

. Scholtz, A. N. A. Mth. 20 (1881) 220-. 
. Zurria, G. Catania Ac. Gioen. At. 8 

(1895) Mm. 3, 24 pp. 
. Macfarlane, A. As. Fr. C. E. (1897) 

(Pt. 2) 147-. 
. Pktkot, A. N. A. Mth. 18 (1899) 65-. 

by aid of a jointed system. Saint-Loup, L. 
C. B. 79 (1874) 1323-. 

circular and hyperbolic functions. 
Matzka, W. Grunert Arch. 37 (1861) 399-. 

, Cockle's. Cayley, A. Camb. and Dubl. 
Mth. J. 6 (1851) 186. 

by differences of roots. Eisenlohr, 0. Crelle 
J. 42 (1852) 236-. 

, expressions occurring in. Eisenstein, G. 

Crelle J. 27 (1844) 319-. 
, formula for. Young, J. R. [1874] Ir. Ac. 

P. 2 (1875-77) 26-. 
, general. Graves, J. T. (vi Adds.) Ph. 

Mg. 13 (1838) 217- 
, , and irreducible case. Penny, W. G. 

Atlantis 3 (1860) 156-. 
, Gierman's. Sintzow, D. Fschr. Mth. 

(1899) 102. 
, indirect (Posselt). Encke, J. F. As. Nr. 

3 (1825) 395-. 

by introducing a perfect cube. Alexandre, R. 
N. A. Mth. 5 (1866) 358-. 



Equations, 3rd order 2430 

solution when one root is known (Lobatto). 
Serret, J. A. Liouv. J. Mth. 14 (1849) 47-. 

without removing 2nd term. Rutherford, W. 
Mathematician 3 (1850) 180-. 

symmetries and irreducible case. Kummell, 

C. H. A. Mth. 6 (1891-92) 179-. 
theorem. Prouhet, E. N. A. Mth. 11 (1852) 

324-. 
theory. Oekinghaus, E. Arch. Mth. Ps. 3 

(1886) 92-. 
, contribution to. Miiller, J. H. T. Grunert 

Arch. 25 (1855) 73-. 
trigonometric expressions for roots. Bjorling, 

E. G. Stockh. Ofv. 7 (1850) 193- ; Grunert 

Arch. 19 (1852) 228-. 

solution. Demongeot, A. N. A. Mth. 20 
(1861) 143-. 

. St Germain, A. de. N. A. Mth. 10 

(1871) 63-. 
two. Cayley, A. Mess. Mth. 22 (1893) 69-. 

Irreducible case. 

Lorgna, A. M. Verona S. It. Mm. 1 (1782) 

707-. 
Stainville, de. Par. EC. Pol. Cor. 3 (1814- 

16) 58-. 
Gretschel, H. Arch. Mth. Ps. 42 (1864) 

431-. 

Meyer, J. Lux. S. Sc. Mm. 8 (1865) 359-. 
Hermann, A. N. A. Mth. 6 (1867) 270-. 
Unferdinger, F. Arch. Mth. Ps. 49 (1869) 

484-. 

Reidt, F. Z. Mth. Ps. 17 (1872) 430-. 
Benthem, A. N. Arch. Wisk. 1 (*1875) 67-. 
Privat, F. C. E. 103 (1886) 774. 
Azzarelli, M. Em. N. Line. At. 40 (1887) 

67-. 

Mollame, V. Nap. Ed. 29 (1890) 167-. 
Holder, O. Mth. A. 38 (1891) 307-. 
Pokrowsky, P. M. Fschr. Mth. (1892) 95. 
Gegenbauer, L. Mh. Mth. Ps. 4 (1893) 155-. 
Kneser, A. Mth. A. 41 (1893) 344-. 
Mollame, V. Nap. Ed. 34 (1895) 111-. 
Hamilton, A. A. Mth. 1 (1900) 41-. 
Cardan's formula, application of trigonometry. 

Zampieri, J. Arch. Mth. Ps. 41 (1864) 60-. 
solution. Nordmark, Z. Ups. N. Acta S. Sc. 

6 (1799) 203-. 
. Kendall, 0. H. Am. J. Mth. 1 (1878) 

285-. 
.non-transcendental. Grunert, J. A. Grunert 

Arch. 30 (1858) 135-. 

when roots are all real, and at least one 
is rational. Weichold, G. Liouv. J. Mth. 
5 (1879) 293-. 



logarithm tables, &c. Veriot, E. C. E. without imaginaries. Peche, F. Haidinger 



66 (1868) 619-, 730-. 
, peculiar algebraic. Miinster, E. N. Mg. 

Ntvd. 19 (1873) 23-. 
, and roots in functions of discriminant 

of cubic. Mollame, V. G. Mt. 16 (1878) 

341-. 

by trigonometric and hyperbolic functions. 
Gronau, J. F. W. Danzig Schr. 6 (Hft. 2 u. 3) 
(1861) 68 pp. 

when one root is known. Lobatto, R. Liouv. 
J. Mth. 9 (1844) 177-. 



Ab. 4 (1851) (Ab. 3) 125-. 
series. Boot extraction. Valz, B. C. E. 

58 (1864) 1186-. 
treatment, Clausen's. Meyer, G. F. Grunert 

Arch. 39 (1862) 235-. 

Equations, 3rd and 4th orders. 

Franke, E. [1880] Crelle J. Mth. 90 (1881) 

102-. 
Halpten, G. H. N. A. Mth. 4 (1885) 17-. 



171 



2430 Equations, 3rd and 4th orders Equations, 4th order 2430 

double system of values in solving. Valles, F. 

C. R. 47 (1858) 30-. 
. Ollive-Meinadier, . Gard 

Mm. Ac. (1859) 171-. 
equation of anharmonic ratios corresponding 

to roots. Painvin, L. N. A. Mth. 19 (I860) 

407-. 
squares of differences of roots. Roberts, 

M. Tortolini A. 2 (1859) 330-. 
. Casey, J. [1874] Ir. Ac. 

P. 2 (1877) 40-. 
. Forestier, C. N. A. Mth. 

2 (1883) 209-. 
factors. Elliott, E. B. Mess. Mth. 25 (1896) 

170-. 
and of 5th. Autonne, L. Par. S. Mth. Bll. 28 

(1900) 90-. 
when J 18 = 0, solution. Faa de Bruno, 

F. Am. J. Mth. 3 (1880) 154-. 
and 6th, solution by trigonometric and 

hyperbolic functions. Heymann, W. Crelle 

J. Mth. 113 (1894) 267-. 

final formula for algebraic solution. Mem- 
man, M. Am. J. Mth. 14 (1892) 237-; N. Y. 

Mth. S. Bll. 1 (1892) 202-, 236. 
general. Boer, F. de. Amst. Ak. Vs. M. 20 

(1884) 413- ; Fschr. Mth. (1884) 79. 
, root formula. Unferdinger, F. Wien Sb. 

50 (1865) (Ab. 2) 225-. 
, solution. Pilatte, . Gergonne A. Mth. 

2 (1811-12) 152-. 

, . Gergonne, J. D. Gergonne A. Mth. 13 

(1822-23) 385-. 
, . Grassmann, H. Arch. Mth. Ps. 51 

(1870) 93-. 
, . Fitz, N. Des Moines Anal. 3 (1876) 

50-. 

_, _. Weichold, G. C. R. 82 (1876) 1093-. 
, . Lodge, A. QJ. Mth. 19 (1883) 257-. 
literal, case. Pagani, G. M. Quetelet Cor. 

Mth. 4 (1828) 291-. 
nature of roots. Lucas, F. Par. S. Mth. Bll. 

18 (1890) 145-. 
with no real root, calculation of roots. Kora- 

lek, P. N. A. Mth. 11 (1852) 117-. 
reality of roots. Desboves, A. H. N. A. Mth. 

3 (1844) 387-. 

reduction. Schlamilch. 0. Schlomilch Z. 8 
(1863) 223-. 

to equation of 3rd order. Hoppe, E. Arch. 
Mth. Ps. 69 (1883) 111-. 

reciprocal equation. Brocard, H. P. P. B. 

(xn) Mathesis 2 (1882) 180-. 
of same order. Alexandre, R. N. 

A. Mth. 5 (1866) 477-. 
2nd order. Ligowski, W. [1879] 

Arch. Mth. Ps. 65 (1880) 426-. 
root forms, domains of the 3. Hoppe, R. Arch. 

Mth. Ps. 14 (1896) 398-. 
roots, Aronhold's formula. Janni, V. G. Mt. 

21 (1883) 213-. 

related to sides of cyclic quadrilateral. 
Matthiessen, L. Z. Mth. Ps. 9 (1864) 453-; 
10 (1865) 331-. 

and of 6th, in theory of conies and quadrics. 

Joachimsthal, F. Crelle J. 53 (1857) 149-. 
solution. Berndtson, B. Stockh. Ac. Hndl. 

28 (1807) 173-. 



Sochocki, J. Prace Mt.-Fiz. 10 (1899-1900) 

135- ; Fschr. Mth. (1899) 102-. 
limit of roots. Fournier-Vannson, . N. A. 

Mth. 11 (1852) 60-. 
literal, solution. Jourdain, . Liouv. J. Mth. 

4 (1859) 205-. 
, . Matthiessen, L. Arch. Mth. Ps. 45 

(1866) 415-. 
problem, solution. Tortolini, B. Rm. At. N. 

Line. 22 (1869) 166-. 
roots of which can be expressed without cubic 

radicals. Realis, S. N. A. Mth. 18 (1879) 

296-. 
solution. Twining, A. C. Silliman J. 9 (1825) 

86-. 
. Sturm, J. B. Grunert Arch. 24 (1855) 

112-. 

. Tortolini, B. Tortolini A. 1 (1858) 310-. 
. Hilt, G. W. Des Moines Anal. 2 (1875) 

4-. 

by construction. Chasles, M. Liouv. J. 
Mth. 20 (1855) 329-; C. R. 41 (1855) 
677-. 

, Lagrange's method. Candioti, M. R. Arg. 
S. Ci. A. 46 (1898) 223-. 

by linear substitution x = . Azza- 

relli, M. Rm. At. N. Line. 24 (1871) 83-. 
same principle. Sommer, B. Grunert 

Arch. 27 (1856) 354-. 
solutions of which by radicals are rational. 

Rummer, E. E. Berl. Ak. Mb. (1880) 

930-. 
Sturmian constants. Cayley, A. QJ. Mth. 4 

(1861) 7-. 
theorem. Desboves, A. C. R. 90 (1880) 



theory. Cockle, Jas. Camb. Mth. J. 3 (1843) 

104-. 
, elementary. Pokrowsky, P. M. Fschr. 

Mth. (1893-94) 152-. 
values of roots when coefficient of first term 

is zero. Faure, H. N. A. Mth. 14 (1855) 

194-. 

Equations, 4th order. 

Bret, . Par. EC. Pol. Cor. 2 (1809-13) 

217-. 
Ampere, A. M. Quetelet Cor. Mth. 9 (1837) 

Roberts, M. N. A. Mth. 18 (1859) 87-. 
Catalan, E. C. , N. A. Mth. 2 (1863) 341-. 
Pokorny, M. Z. Mth. Ps. 10 (1865) 320-. 
Ball, R. S. QJ. Mth. 7 (1866) 6-, 358-. 
Enneper, A. Z. Mth. Ps. 18 (1873) 93-. 
Rawson, R. Manch. Lt. Ph. S. P. 19 (1880) 

127-. 
Oekinghaus, E. Arch. Mth. Ps. 6 

169-. 

Gordan, P. Mth. A. 29 (1887) 318-. 
Darbi, G. G. Mt. 38 (1900) 153-. 
analytical solution. Valeriani, V. G. Mt. ["13 

(1875)] 99-. 
case of reduction to canonical form. Gru- 

zintsev, A. P. (xn) Kharkov Mth. S. Com. 

(1881) 116-. 
class. Brioschi, F. C. R. 57 (1863) 106-. 



172 



2430 



Equations, 4th order, continued. 

solution. Anon, (vi 1231) Tilloch Ph. Mg. 

52 (1818) 378-. 
. Greatheed, S. S. [ascribed to Gregory, 

D. F., in vol. m]. Camb. Mth. J. 1 (1839) 

254-. 

. Graves, C. Ir. Ac. P. 3 (1847) 111-. 
. Peche, F. Haidinger B. 3 (1847) 19-. 
. Grunert, J. A., & Schlesicke, W. Grunert 

Arch. 12 (1849) 166-. 
. Lindman, C. F. Grunert Arch. 23 (1854) 

435-. 

. Armhold, S. H. Crelle J. 52 (1856) 95-. 
. Grunert, J. A. Grunert Arch. 31 (1858) 

476-. 

. Hermite, C. C. E. 46 (1858) 715-. 
. Spitz, C. Grunert Arch. 33 (1859) 442-. 
. Schlomilch, 0. Schlomilch Z. 6 (1861) 

49-; Liouv. J. Mth. 8 (1863) 99-. 
. Matthiessen, L. Schlomilch Z. 8 (1863) 

133-, 140- ; Arch. Mth. Ps. 41 (1864) 231-. 
. Bellavitis, G. N. A. Mth. 3 (1864) 

121-. 
. Darboux, G. Liouv. J. Mth. 18 (1873) 

220-. 
. Dixon, T. S. E. Am. J. Mth. 1 (1878) 

283-. 

. Briot, F. N. A. Mth. 20 (1881) 225-. 
. Borenius, G. [1882-83] Helsingf. Acta 12 

(1883) 653- ; Stockh. Ak. Hndl. Bh. 9 (1884- 

85) No. 4, 18 pp. 

. Sawin, A. M. A. Mth. 1 (1884-85) 14. 
. Eastorguev, D. Kazan S. Nt. (Ps.-Mth.) 

P. 4 (1886) 236-. 
. McClintock, E. N. Y. Am. Mth. S. fill. 

3(1897)389-; 4(1898)283. 
. Starkweather, G. P. N. Y. Am. Mth. S. 

fill. 4 (1898) 524-. 
. Valentiner, H. N. Ts. Mth. 9 (B) (1898) 

36-. 
, Ampere's. Grunert, J. A. Grunert Arch. 

1 (1841) 16-. 

by elliptic functions. Lebesgue, V. A. 
Liouv. J. Mth. 3 (1858) 391-. 

, Euler's. Strehlke, F. Crelle J. 12 (1834) 

358-. 
, general. Schlesicke, W. Grunert Arch. 16 

(1851) 58-. 
, . Grunert, J. A. Grunert Arch. 40 

1863) 394-. 
, . Nett, A. M. Arch. Mth. Ps. 56 (1874) 

407-. 

by homographic relation between roots. 
Imseneckij, V. G. Kharkov Mth. S. Com. 3 
(1893) 257- ; Fschr. Mth. (1893-94) 153. 

, method, and application to equations of 

higher orders. Perrin, R. Par. S. Mth. Bll. 

10 (1882) 139-. 
, Schloemilch's. Meyer, G. F. Grunert 

Arch. 39 (1862) 230-. 
, and some algebraic theorems. Hermite, C. 

C. E. 46 (1858) 961-. 

without removal of 2nd term. Grunert, J. A. 
Grunert Arch. 39 (1862) 198-. 

, Wronski's. Gergonne, J. D. Gergonne A. 

Mth. 3 (1812-13) 137-, 206-. 
solutions, various. Dippe, M. C. Grunert 

Arch. 7 (1846) 334-. 



Equations of the lower orders, etc. 



2430 

and Sturm's theorem. Kanig, J. F. Grunert 

Arch. 34 (I860) 101-. 
trigonometric expressions for roots. Bjorling, 

E. G. Stockh. Ofv. 7 (1850) 233-; Grunert 

Arch. 19 (1852) 297-. 
solution. Oekinghaus, E. Arch. Mth. Ps. 

70 (1884) 133-. 



Equations, order above 4th, solution in par- 
ticular cases. Ruffini, P. [18011 Mod. S. It. 

Mm. 9 (1802) 444-. 
of nth order with only 2 real roots. Andre, 

D. C. E. 98 (1884) 417-. 
. Sylvester, J. J. 

C. E. 98 (1884) 550-. 
Irrationality J (a + *Jb). Azzarelli, M. Em. 

N. Line. At. 38 (1885) 227-. 
Particular equations of various orders, solu- 
tion. Stem, A. Mth. Ts. 2 (1860) 45-. 
Planets, mutual distance of 2, roots of equation 

obtained by equating to zero. Cauchy, A. L. 

C. E. 19 (1844) 1228-. 
"Problem of the lights." Parker, W. H. 

Camb. (M.) Mth. M. 1 (1859) 160-. 
(Parker). Runkle, J. D. Camb. 

(M.) Mth. M. 1 (1859) 178-. 
Eeciprocal equations. Gamier, J. G. Quetelet 

Cor. Mth. 2 (1826) 153-. 
. Comberousse, C. de. N. A. Mth. 8 (1889) 

27-. 

. Gianni, L. G. Mt. 30 (1892) 206-. 

and equations of 4th order. Pellet, A.E. 

N. A. Mth. 13 (1894) 108-. 
, equations reducible to. Fischer, F. W. 

Arch. Mth. Ps. 55 (1873) 294-. 
, lowering degree of. Biehler, C. N. A. 

Mth. 6 (1887) 251-. 
, theory. Vogt, A. Arch. Mth. Ps. 44 

(1865) 50-. 
, . Studnidka, F. J. Casopis 19 (1890) 

1-; Fschr. Mth. (1890) 110-. 
Eesol vents, first, of equation of 4th order 



and of equation of 3rd order 

ay 3 + 3by 2 + Bey + m = 0. 

Rawson, R. Manch. Lt. Ph. S. P. 20 (1881) 

144-. 
Eoots of equation x* + 2 = 0. Terquem, 0. N. 

A. Mth. 4 (1845) 518-. 
"Eule of false" of the Arabians, and direct 

solution of literal equations of 2nd and 3rd 

orders. Matthiessen, L. Z. Mth. Ps. 15 

(1870) 41-. 
" " and equations of 2nd order. 

Castro, M. Mex. Eeg. Trim. 1 (1832) 

125-. 
Trigonometrical solution of certain equations. 

Pellet, A. As. Fr. C. E. (1889) (Ft. 2) 

164-. 

Trinomial Equations. 

Marrecas Ferreira, L. F. G. Teix. J. Sc. 5 

(*1883) 50-. 
Catalan, E. Brux. Ac. Bll. 13 (1887) 414-. 



173 



2440 



Numerical solution of equations 



Trinomial equations, continued. 
Nekrassoff, P. Mth. A. 29 (1887) 413-. 
class. Besso, D. Em. E. Ac. Line. Mm. 19 

(1884) 631- . 
of form x* n+l -x- k = 0, n prime. Berndtson, 

B. Gergonne A. Mth. 11 (1820-21) 373-. 
x n AxB = Q. Casinelli, A. Bologna 

N. Cm. 7 (1844) 331-. 
X 2n+i - x =k. Genocchi, A. Tortolini A. 

2 (1859) 253-. 
x r + ax + b=Q. Thiele, T. N. Mth. Ts. 

1 (1859) 115-. 
y*+py + q = Q. Borden, J. Des Moines 

Anal. 5 (1878) 41-. 
u m _pyn - q = Q, Nekrasov, P. A . [1879- 

82] (xn) Eec. Mth. (Moscou) 11 (1883-84) 

t n + at n ~ s +b 0, a solution. Heymann, 

W. Z. Mth. Ps. 31 (1886) 223-. 
u m - pu n -q = 0, theory. Nekrasov, P. A . 

[1894] Eec. Mth. (Moscou) 17 (1895) 439-; 

Fschr. Mth. (1893-94) 162. 
Gauss's method of lowering. Montucci, H. 

C. E. 70 (1870) 445-. 

solution. Nell, A. M. Arch. Mth. Ps. 1 
(1884) 311-. 

general, roots. Farkas, G. (xn) Mag. Tud. 
Ak. Ets. 12 (No. 5) (1878) 116. 

nature of roots. Bonnet, 0. N. A. Mth. 4 
(1845) 293-. 

of odd order X m X= R, solution by means of 
new algebraic sign. Piarron de Mondesir, 
E. S. As. Fr. C. E. (1877) 168-. 

and quadrinomial, elementary treatment. Hey- 
mann, W. Z. Mth. Ps. 37 (1892) 90-. 

of 7th order in particular. Besso, D. Em. E. 
Ac. Line. Ed. 1 (1885) 237-. 

solution. Gamier, J. G. Brux. Ac. Bll. 6 
(1839) 474-. 

. Tetmajer, J. (xn) Krk. Ak. (Mt.-Prz.) 
Pam. 5 (1880) 1-. 

by algorithms resembling continued fractions. 
Hoffmann, K. E. [1880] Arch. Mth. Ps. 66 
(1881) 33- . 

theory. Heymann, W. Mth. A. 28 (1887) 
61. 



2440 



Vincent, A. J. H. Lille Mm. S. (1833) 1-; 

(1838) 5-. 

Dirksen, E. H. Crelle J. 14 (1835) 316-. 
Sturm, J. C. F. Par. Mm. Sav. Etr. 6 (1835) 

271-. 

Kupfer, K. (xn) Mosc. Un. Mm. 12 (1836) 256-. 
Cauchy, A. L. C. E. 11 (1840) 829-. 
Encke, J. F. Berl. As. Jb. (1841) 281-. 
Libri, G. C. E. 17 (1843) 93-. 
Martynowski, J. Liege Mm. S. Sc. 1 (1843) 

290- ; 2 (1845-46) 445-; 8 (1853) 20-. 
Adeler, . Bordeaux Ac. Act. (1844) 449-. 
Galois, E. Liouv. J. Mth. 11 (1846) 397-. 
Vdllas, A. (xn) [Mag. Ak. Ets. (1850)] 39-. 
Bellavitis, G. Yen. At. 3 (1852) 120-. 
Mdbius, A. F. Leip. B. (1852) 1-. 
Valz, B. C. E. 41 (1855) 685-. 
Bellavitis, G. (vi Adds.) Yen. Mm. I. 6 (1856) 

357. 

Dupre, A. C. E. 45 (1857) 585-. 
Bellavitis, G. Yen. Mm. I. 9 (1860) 177-. 
Denzler, W. Ziir. Yjschr. 5 (1860) 384-; 6 



Oliveira, C. B. Ev. Brazil. 3 (1860) 185-. 

Janni, V. G. Mt. 5 (1867) 182-. 

Woolhouse, W. S. B. [1868-70] L. Mth. S. 

P. 2 (1869) 75- ; I. Act. J. 15 (* 1870) 313-. 
De Morgan, A. [1868-70] L. Mth. S. P. 2 

(1869) 84- ; I. Act. J. 15 (*1870) 327-. 
Schroder, E. [1869] Mth. A. 2 (1870) 317-. 
Vecchi, S. II Polit. 20 (1872) 370-. 
Siebel, A. Arch. Mth. Ps. 56 (1874) 422- ; 57 

(1875) 73-, 350- ; 58 (1876) 127- ; 60 (1877) 

138- ; 61 (1877) 122- ; 65 (1880) 394-; 67 

(1882) 375-. 

Collignon, E. As. Fr. C. E. 4 (1875) 200-. 
Houzeau, J. C. Brux. Ac. Bll. 40 (1875) 455-. 
Janni, V. Nap. Ed. 17 (1878) 138-. 
Laguerre, E. N. A. Mth. 17 (1878) 20-, 97-. 
Amstein, H. Laus. S. Yd. Bll. 20 (1885) 

201-. 

Netto, E. Mth. A. 29 (1887) 141-. 
Carvallo, E. Toul. Fac. Sc. A. 3 (1889) 0, 

40pp. 

Phragme'n, E. Stockh. Ofv. (1892) 179-. 
Sdderblom, A. Goteb. Hndl. 2 (1899) 105-. 



2440 Numerical solution of equa- 
tions (including graphical me- 
thods). 

Numerical solution of equations in general. 

Caluso, (I'abbe) T. V. de. Turin Mm. Ac. 6 

(1792-1800) 159-. 
Cassella, G. [1803] Mod. Mm. S. It. 11 (1804) 

203-. 
Btrard, . Gergonne A. Mth. 10 (1819-20) 

61-. 
Dandelin, G. P. Brux. Mm. Ac. Sc. 3 (1826) 

7-, 153-. 
Timmermans, J. A. Quetelet Cor. Mth. 2 

(1826) 218-. 
Galois, E. Fe'russac Bll. Sc. Mth. 13 (1830) 

413-. X ' 



Approximate determination of roots. 

Fourier, J. B. J. Par. S. Phlm. Bll. (1818) 

61-. 

Horner, W. G. Phil. Trans. (1819) 308-. 
Gilbert, D. QJ. Sc. 14 (1823) 353-. 
Crelle, A. L. Berl. Ab. (1835) 263-. 
Ostrogradsky, H. A. [1835] St Pet. Ac. Sc. 

Bll. 1 (1836) 1-; St Pet. Ac. Sc. Mm. 3 

(pte. 1) (1838) 233-. 
Libri, G. C. E. 4 (1837) 168-. 
Frisiani, P. Mil. Effem. As. (1847) 3-. 
Grunert, J. A. Grunert Arch. 20 (1853) 337-. 
Sornin, J. Toul. Mm. Ac. 1 (1857) 26-. 
Grunert, J. A. Grunert Arch. 30 (1858) 54-. 
Genocchi, A. N. A. Mth. 20 (1861) 48-. 
Michaelis, J. P. Lux. S. Sc. Mm. 7 (1864) 

143-. 
Sang, E. [1864] Edinb. E. S. P. 5 (1866) 

162-. 



174 



2440 



Numerical solution of equations 



2440 



Approximate determination of roots, continued. 
A. Q. G. C. Mess. Mth. 4 (1868) 132-. 

D g. Ts. Mt. Fys. 4 (1871) 201-. 

Laguerre, . N. A. Mth. 3 (1884) 113-. 
Bugaev, N. V. [1894] Eec. Mth. (Moscou) 18 

(1896) 289- ; Fschr. Mth. (1896) 70-. 
Laisant, C. A. As. Fr. C. B. (1895) (Ft. 2) 

220- . 
Bugaev, N. V. [1896] Eec. Mth. (Moscou) 19 

(1897) 421 (bis)- ; Fschr. Mth. (1897) 96. 
Lemeray, E. M. N. A. Mth. 17 (1898) 534-. 
of cubic equations by continued fractions. 

Sang, E. Edinb. E. S. P. 32 (1887) 311-. 

(1 + p) n 1 

equation A = v 2 . Ryley, E. Assur. 

Mg. [1 (* 1851)] 332-. 
with real roots only. Laguerre, E. C. 

E. 79 (1874) 522-; N. A. Mth. 19 (1880) 
161-, 193-. 

(Laguerre). Hermite, C. 

Em. N. Line. Mm. 3 (1888) 155-. 
( ). Borel, E. fill. Sc. 

Mth. 22 (1898) 11-. 
imaginary roots. Bonnet, 0. N. A. Mth. 4 

(1845) 164-, 388-; 12 (1853) 243-. 

, Lagrange's method. Cavalieri San- 
Bertolo, N. Em. At. 4 (1850-51) 1-. 

incommensurable roots. Fauche-Prunelle, A, 

Grenoble Ac. Delph. Bll. 1 (1846) 563-. 
irrational roots. Voll, W. Oken Isis (1826) 

490-. 
real roots. Piobert, . N. A. Mth. 10 (1851) 

174-. 

. Buchwaldt, F. Mth. Ts. 2 (1860) 73-. 

. Janni, G. G. Mt. 8 (1870) 157-. 

of equation x n +px + q = 0. Kjeldgaard, 

A. {xn) Ts. Mth. 4 (1880) 135-. 
, methods of Cauchy and Newton. Moigno, 

F. N. A. Mth. 10 (1851) 14-. 

in series of aliquot parts. Homer, J. QJ. 

Mth. 3 (1860) 251-. 
Simpson's method. Pessuti, G. [1806] Mod. 

S. It. Mm. 13 (1807) 193-. 
singular case. Gergonne, J. D. Gergonne A. 

Mth. 10 (1819-20) 122-. 



Budan's method. Gergonne, J. D. Gergonne 

A. Mth. 4 (1813-14) 115-. 
. Ferroni, P. [1823] Mod. S. It. Mm. 20 

(1828) 17-. 
Cauchy 's modification of Newton's method. 

Housel, . N. A. Mth. 15 (1856) 244-. 
Continued fractions applied to determining 

two roots simultaneously. Matthiessen, L. 

Schlomilch Z. 6 (1861) 51-. 
, solution by. Homer, W. G. QJ. Sc. 

21 (1826) 72-, 282-; 22 (1827) 67-, 285-. 
, . Grebe, E. W. Grunert Arch. 10 

(1847) 345-; 16 (1851) 261-. 
, . Gomes Teixeira, F. (x) Lisb. J. 

Sc. Mth. 4 (1873) 89-. 
, . Giinther, S. [1873] (vn) Mth. 

A. 7 (1874) 262-. 
Convergence of certain series in numerical 

solution of equations. Graeffe, C. H. Crelle 

J. 10 (1833) 288-. 



Convergence of series of approximations to 
roots of equations. Lemeray, E. M. As. 
Fr. C. E. (1894) (Pt. 2) 252-. 

for root by Lagrange's theorem. 
Cauchy, A. L. C. E. 23 (1846) 493-. 

Definite integrals, expression of roots of tri- 
nomial equations by. Lachtin, L. [1889] 
Eec. Mth. (Moscou) 15 (1891) 61-. 

, solution by. Jacobi, C. G. J. Crelle 

J. 2 (1827) 1-. 

, . Hoppe, E. Schlomilch Z. 3 

(1858) 173-. 

, . Kretkowski, W. [1881] (xn) Krk. 

Ak. (Mt.-Prz.) Pam. 7 (1882) 158-. 

Derived functions and numerical solution of 
equations. Mlasojedov, A. N. Eec. Mth. 
(Moscou) 12 (1885) 757- ; Fschr. Mth. (1886) 

Differential equations, solution by. Heymann, 
W. Z. Mth. Ps. 31 (1886) 102-, 129-. 

Eisenstein's theorem on series for root of 
algebraic equation. Hermite, C. L. Mth. 
S. P. 7 (1875-76) 173-. 

. Gomes Teixeira, F. 

Arch. Mth. Ps. 3 (1886) 315-. 

Equation A = (l + x) m (l + bx), numerical solu- 
tion, x being a small fraction. Badell, . 
Grunert Arch. 2 (1842) 122-. 

= (-)(-). . Lind- 

man, C. F. Grunert Arch. 23 (1854) 445-. 

Equations a 2 + fee = 16, 6 2 + ac=17, c 2 + o6=18, 
approximate solution. Bute, . Thomson 
A. Ph. 5 (1815) 53-. 

in Bangma's "Algebra voor de Scholen." 
Schmidt, J. B. Amst. Mengelwerk 2 (1816) 
153-. 

, continued fractions for whose roots terminate 

in same quotients. Serret, J. A. Liouv. J. 

Mth. 15 (1850) 152-. 
, order of which is power of prime number. 

Betti, E. Tortolini A. 6 (1855) 260- ; C. E. 

48 (1859) 182-. 
, . Mathieu, E. 

Tortolini A. 4 (1861) 113-. 

with secondary (imaginary) roots. Zielinski, 
A. Des Moines Anal. 3 (1876) 52-. 

, 2nd order, exhibition of both roots in one 

series of converging fractions. Sang, E. 

Edinb. E. S. P. 4 (1862) 70-. 
, , solution by continued fractions. 

Lebesgue, V. A. Liouv. J. Mth. 5 (1840) 

281-. 
, , successive approximation, cases. 

St Germain, A. de. N. A. Mth. 13 (1874) 

401-. 
, , where coefficient of x 2 is small. 

Gerono, G. C. N. A. Mth. 16 (1857) 436-. 
, 3rd order, development of roots in continued 

fractions. Sarrus, F. Gergonne A. Mth. 10 

(1819-20) 189-. 
, , irreducible case, development of 

roots in continued fraction. Clausen, T. 

As. Nr. 19 (1842) 241- ; Grunert Arch. 2 

(1842) 446- (with additions by Grunert). 
, , numerical solution. Maulbon 

d'Arbaumont, . Epinal (Vosg.) A. 2 (1834) 

637-. 



175 



2440 



Equations, 3rd order, numerical solution. 

Lindman, C. F. Stockh. Ofv. 11 (1854) 333-; 

Grunert Arch. 25 (1855) 290-. 
, , . Burnier, F. Laus. Bll. S. 

Vd. 10 (1868-70) 591-. 
, , . Catania, S. Bv. Mt. 5 (1895) 

81-. 
, , roots as continued fractions. Marcher, 

. Grunert Arch. 39 (1862) 39-. 
, , x 3 - 2x - 5 = 0, solution to 153 figures. 

Hicks, J. P. [1850] Camb. Ph. S. T. 10 

(1864) 337. 
below 4th order, numerical solution. Warner, 

J. D. Am. As. P. (1880) 267-. 
, 4th order, numerical solution. Choquet, C. 

N. A. Mth. 3 (1844) 439. 
, , . Vidal, V. N. A. Mth. 17 

(1878) 367-. 
, 5th order, and some others, numerical 

solution. Montucci, H. C. B. 60 (1865) 

440- ; 61 (1865) 31-. 
Form of roots. Hill, C. J. D. Ups. N. Acta 

S. Sc. 2 (1856) 221-. 
Four roots of numerical equation, finding. 

Riedl von Leuenstern, J. Tortolini A. 6 

(1855) 481-. 

Graffe's solution. Hansen, H. J. Ts. Mth. 5 

(1887) 169-. 

Horner's method. De Morgan, A. Mathe- 
matician 3 (1850) 289-. 
. Matzka, W. [1871] Prag Ab. 5 (1872) 

47pp. 
, proof. Jenkins, M. Mth. Gz. No. 6 

(1895) 55-. 
Imaginary roots, determination. Poletti, G. 

[1823-28] Tor. Mm. Ac. 30 (1826) 49- ; 35 

(1831) 77-. 
, . Bellavitis, G. [1845] Yen. Mm. I. 

3 (1847) 109-. 

, . Buchwaldt, F. Mth. Ts. 2 (1860) 177-. 

, . Bellavitis, G. [1864] (vn) Ven. 

Mm. I. 11 (1862) 461-. 
, . Yvon-Villarceau, A. J. F. C. B. 

86 (1878) 1427-. 
, . Farkas, J. C. E. 87 (1878) 791-, 

1027- ; 88 (1879) 273-, 565-. 
, by recurring series. Frisiani, P. Mil. 

Effern. As. (1850) 3-. 
Infinite series, solution by. Multedo, . 

Geneva Mm. Ac. 3 (1814) 108-. 
, . Jacobi, C. G. J. Crelle J. 6 

(1830) 257-. 
, .' Heegmann, A. [1861-64] (xn) 

Lille S. Mm. 8 (1862) 217- ; 2 (1866) 1-. 
, . Dietrich, R. Arch. Mth. Ps. 69 

(1883) 337-. 

Integer roots of equation with integral co- 
efficients. Gerono, G. C. N. A. Mth. 15 

(1856) 449-. 

Lagrange's treatise. Raabe, J. L. Crelle J. 17 

(1837) 94-; 20 (1840) 57-. 
Logarithmic solution. Garnett, J. Am. Ph. 

S. T. 6 (1809) 391-. 
. Zenger. C. V. As. Fr. C. E. (1885) 

(Pt. 2) 91-. 
Method of differences. Matrot, A. [18751 (xn) 

Lille S. Mm. 2 (1876) 7-. 



Numerical solution of equations 2440 

Weddle, T. E. S. P. 4 (1841) 



Method, new. 
300-. 

, . Lalanne, L. L. C. C. B. 81 (1875) 
1186-, 1243- ; 82 (1876) 1487-. 

, . Eggers, H. Des Moines Anal. 3 (1876) 
149-. ' 

Methods, two simple. Giesen, A. Z. Mth. Ps. 

23 (1878) 35-. 
Newton's method of approximation. Gergonne, 

J. D. Gergonne A. Mth. 20 (1829-30) 196-. 
---- . Anne,L. N. A. Mth. 5 (1846) 116-. 
---- . Lemonnier, H. N. A. Mth. 1 

(1862) 188-, 243-. 

---- . Genocchi,A. G. Mt. 2 (1864) 27-. 
---- . Thomson, F. D. [1864] Mess. 

Mth. 3 (1866) 40-. 
---- . Piani, D. Bologna Ac. Sc. Mm. 

6 (1866) 69-. 
---- . Darboux, G. N. A. Mth. 8 (1869) 

-- ' -- . Franklin, F. Am. J. Mth. 4 

(1881) 275-. 
---- . Fouret, G. N. A. Mth. 9 (1890) 

567-. 

. Berg, F. J. van den. Amst. 
Ak. Vs. M. 9 (1892) 53-; Fschr. Mth. (1892) 
103-. 

---- . Malo, E. N. A. Mth. 11 (1892) 

169-. 
---- . Tauber, A. Mh. Mth. Ps. 6 

(1895) 291-. 



and that of proportional parts, 
comparison. Maleyx, L. N. A. Mth. 18 
(1879) 218-. 



- solution. Baltzer, R. Leip. B. 18 (1866) 358-. 
Numerical and algebraic solution of equations. 

Anon, (vi 564) Gergonne A. Mth. 20 (1829- 

30) 352-. 

---- . Biasi, G. [1876] Epm. 

Mth. 1 (1877) 315-. 

equation, problem. Koralek, P. N. A. 
Mth. 13 (1854) 36-. 

equations. Vallas, A. Camb. (M.) Mth. 
M. 3 (1860) 10-. 

--- . Laguerre, E. C. E. 79 (1874) 996-. 
-- and analytical geometry in space. Zmurko , 

L. [1869] Wien D. 30 (1870) (2te Ab.) 217-. 
-- depending on expressions of 1st degree. 

Serdoblnskii, V. E. [1874] (xn) Eec. Mth. 

(Moscou) 7 (1874-75) (Pt. 1) 263-. 
-- of even degree, analysis, improvement. 

Young, J. R. Ph. Mg. 34 (1849) 413-. 
-- with given number of imaginary roots, 

determination. Laguerre, E. C. E. 90 (1880) 

180-. 
. -- having integer roots. Talbot, W. H. F. 

[1875] Edinb. E. S. T. 27 (1876) 303-. 
-- , higher order, one or more unknowns, 

theorems. Spitzer, S. [1849] Haidinger 

Ab. 3 (1850) (Ab. 2) 143-. 
-- and quadratic factors. Finck, B. Liouv. 

J. Mth. 10 (1845) 171-. 
-- , theory. Lepriol, C. J. Eouen Tr. Ac. 

(1812) 41-. 
-- , . Laguerre, E. C. E. 78 (1874) 

278-; Liouv. J. Mth. 9 (1883) 99-; Acta 

Mth. 4 (1884) 97-. 



176 



2440 



Numerical solution of equations 



Principle of proportional parts. Biffignandi, 
A. Acireale Ac. At. 2 (1891) 62-. 

Quadrinomial equations, solution by series. 
Amanzio, D. G. Mt. 14 (1876) 153-, 306-. 

equations, calculation of real roots. Wiener, 
A. Z. Mth. Ps. 31 (1886) 65-, 192. 

Eational roots of numerical equations, new 

method of finding. Moon,E. [1849] Camb. 

Ph. S. P. 1 (1866) 79-. 
Eeal and imaginary roots of numerical equa- 

tion of higher order. Spitzer, S. Haidinger 

Ab. 3 (1850) (Ab. 2) 109-. 

root of equation, series expressing. Bras- 
sinne, E. Toul. Mm. Ac. 6 (1849) 10-. 

roots, calculation. Buchioaldt, F. Mth. Ts. 
3 (1861) 185-. 

-- , . Margerie, C. N. A. Mth. 3 (1884) 

33-. 
-- , by infinite series. Wallinowsky, . 

Crelle J. 33 (1846) 164-. 
-- , development in series. Yvon-Villarceau, 

A. J. F. Liouv. J. Mth. 4 (1878) 119-. 
-- of equation with real coefficients. Giu- 

dice, F. Palermo Cir. Mt. Ed. 1 (1887) 

69-. 

, Moth's determination. Stampfer, S. 
Wien Sb. 1 (1848) 194-. 

-- , simplest method for obtaining. Bella- 

vitis, G. [1845] Ven. Mm. I. 3 (1847) 

109-. 
Eecurring series, solution by. Perrin, E. C. 

E. 119 (1894) 990-, 1190-, 1257-. 
-- , -- . Capelli, A. Nap. Ed. 34 (1895) 

194-. 
-- , -- , extension of D. Bernoulli's theo- 

rem. Mainardi, G. A. Sc. Lomb. Ven. 9 

(1839) 273-; 10 (1840) 113-. 
Eeversion of series, application. Hagen, J. G. 

Am. Ph. S. P. 21 (1884) 93-. 
Eoots of equation, development in series. 

Cauchy, A. L. C. E. 38 (1854) 1105-. 
--- , --- . Antanzio, D. Nap. Ed. 

16 (1877) 122-, 143-. 
--- , --- . Eunge, C. Acta Mth. 6 

(1885) 305-. 
--- , --- . Madsen, N. Ts. Mth. 

5 (1887) 129- ; Fschr. Mth. (1887) 74. 
--- , --- . Fabre, A. As. Fr. C. E. 

(1894) (Pt. 2) 149-. 
--- , -